Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{-5{x}^{{sin(2x + 1)}^{5}}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{-5{x}^{sin^{5}(2x + 1)}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{-5{x}^{sin^{5}(2x + 1)}}\right)}{dx}\\=&e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))\\=&-50{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{4}(2x + 1)cos(2x + 1) - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -50{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{4}(2x + 1)cos(2x + 1) - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x}\right)}{dx}\\=&-50({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{4}(2x + 1)cos(2x + 1) - 50{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{4}(2x + 1)cos(2x + 1) - \frac{50{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{(x)} - 50{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*4sin^{3}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1) - 50{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{4}(2x + 1)*-sin(2x + 1)(2 + 0) - \frac{5*-{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{2}} - \frac{5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{5}(2x + 1)}{x} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0)}{x}\\=&-500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} + 2500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) + \frac{500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x} - 400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{3}(2x + 1)cos^{2}(2x + 1) + 100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{5}(2x + 1) + \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{2}} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{2}} + \frac{25{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} + 2500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) + \frac{500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x} - 400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{3}(2x + 1)cos^{2}(2x + 1) + 100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{5}(2x + 1) + \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{2}} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{2}} + \frac{25{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{2}}\right)}{dx}\\=&-500({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) - 500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) - \frac{500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*2ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{(x)} - 500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)*8sin^{7}(2x + 1)cos(2x + 1)(2 + 0)cos^{2}(2x + 1) - 500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)*-2cos(2x + 1)sin(2x + 1)(2 + 0) - \frac{100*-{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{100({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x(x)} - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*9sin^{8}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x} - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)*-sin(2x + 1)(2 + 0)}{x} + 2500({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) + 2500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) + \frac{2500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*2ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{(x)} + 2500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)*8sin^{7}(2x + 1)cos(2x + 1)(2 + 0)cos^{2}(2x + 1) + 2500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)*-2cos(2x + 1)sin(2x + 1)(2 + 0) + \frac{500*-{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{500({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} + \frac{500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} + \frac{500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x(x)} + \frac{500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*9sin^{8}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x} + \frac{500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)*-sin(2x + 1)(2 + 0)}{x} - \frac{100*-{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{100({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x} - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{4}(2x + 1)cos(2x + 1)}{x} - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*4sin^{3}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x} - \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)*-sin(2x + 1)(2 + 0)}{x} - 400({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{3}(2x + 1)cos^{2}(2x + 1) - 400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{3}(2x + 1)cos^{2}(2x + 1) - \frac{400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{3}(2x + 1)cos^{2}(2x + 1)}{(x)} - 400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*3sin^{2}(2x + 1)cos(2x + 1)(2 + 0)cos^{2}(2x + 1) - 400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{3}(2x + 1)*-2cos(2x + 1)sin(2x + 1)(2 + 0) + 100({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{5}(2x + 1) + 100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{5}(2x + 1) + \frac{100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{(x)} + 100{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0) + \frac{5*-2{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{3}} + \frac{5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{2}} + \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{5}(2x + 1)}{x^{2}} + \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0)}{x^{2}} - \frac{5*-2{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{3}} - \frac{5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{2}} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{10}(2x + 1)}{x^{2}} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*10sin^{9}(2x + 1)cos(2x + 1)(2 + 0)}{x^{2}} + \frac{25*-2{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{3}} + \frac{25({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{2}} + \frac{25{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{10}(2x + 1)}{x^{2}} + \frac{25{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*10sin^{9}(2x + 1)cos(2x + 1)(2 + 0)}{x^{2}}\\=&-5000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) - \frac{4200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x} + 75000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) + \frac{21000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x} - 12000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{7}(2x + 1)cos^{3}(2x + 1) + 3000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{9}(2x + 1)cos(2x + 1) + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{1500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{22500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} + \frac{2250{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - 125000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) - \frac{37500{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{750{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} + 60000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{7}(2x + 1)cos^{3}(2x + 1) - 15000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{9}(2x + 1)cos(2x + 1) - \frac{3750{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x} + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{1200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{3}(2x + 1)cos^{2}(2x + 1)}{x} + \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x} - 2400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{2}(2x + 1)cos^{3}(2x + 1) + 2600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{4}(2x + 1)cos(2x + 1) + \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x} - \frac{10{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{3}} + \frac{15{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{3}} - \frac{75{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{3}} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{3}} + \frac{75{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{3}} - \frac{125{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -5000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) - \frac{4200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x} + 75000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) + \frac{21000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x} - 12000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{7}(2x + 1)cos^{3}(2x + 1) + 3000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{9}(2x + 1)cos(2x + 1) + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{1500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{22500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} + \frac{2250{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - 125000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) - \frac{37500{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{750{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} + 60000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{7}(2x + 1)cos^{3}(2x + 1) - 15000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{9}(2x + 1)cos(2x + 1) - \frac{3750{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x} + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{1200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{3}(2x + 1)cos^{2}(2x + 1)}{x} + \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x} - 2400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{2}(2x + 1)cos^{3}(2x + 1) + 2600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{4}(2x + 1)cos(2x + 1) + \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x} - \frac{10{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{3}} + \frac{15{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{3}} - \frac{75{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{3}} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{3}} + \frac{75{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{3}} - \frac{125{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{3}}\right)}{dx}\\=&-5000({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) - 5000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) - \frac{5000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*3ln^{2}(x)sin^{12}(2x + 1)cos^{3}(2x + 1)}{(x)} - 5000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)*12sin^{11}(2x + 1)cos(2x + 1)(2 + 0)cos^{3}(2x + 1) - 5000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)*-3cos^{2}(2x + 1)sin(2x + 1)(2 + 0) - \frac{4200*-{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{4200({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{4200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{4200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{8}(2x + 1)cos^{2}(2x + 1)}{x(x)} - \frac{4200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*8sin^{7}(2x + 1)cos(2x + 1)(2 + 0)cos^{2}(2x + 1)}{x} - \frac{4200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)*-2cos(2x + 1)sin(2x + 1)(2 + 0)}{x} + 75000({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) + 75000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) + \frac{75000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*3ln^{2}(x)sin^{12}(2x + 1)cos^{3}(2x + 1)}{(x)} + 75000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)*12sin^{11}(2x + 1)cos(2x + 1)(2 + 0)cos^{3}(2x + 1) + 75000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)*-3cos^{2}(2x + 1)sin(2x + 1)(2 + 0) + \frac{21000*-{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + \frac{21000({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x} + \frac{21000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x} + \frac{21000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{8}(2x + 1)cos^{2}(2x + 1)}{x(x)} + \frac{21000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*8sin^{7}(2x + 1)cos(2x + 1)(2 + 0)cos^{2}(2x + 1)}{x} + \frac{21000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)*-2cos(2x + 1)sin(2x + 1)(2 + 0)}{x} - 12000({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{7}(2x + 1)cos^{3}(2x + 1) - 12000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{2}(x)sin^{7}(2x + 1)cos^{3}(2x + 1) - \frac{12000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*2ln(x)sin^{7}(2x + 1)cos^{3}(2x + 1)}{(x)} - 12000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)*7sin^{6}(2x + 1)cos(2x + 1)(2 + 0)cos^{3}(2x + 1) - 12000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{7}(2x + 1)*-3cos^{2}(2x + 1)sin(2x + 1)(2 + 0) + 3000({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{9}(2x + 1)cos(2x + 1) + 3000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{2}(x)sin^{9}(2x + 1)cos(2x + 1) + \frac{3000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*2ln(x)sin^{9}(2x + 1)cos(2x + 1)}{(x)} + 3000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)*9sin^{8}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1) + 3000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{9}(2x + 1)*-sin(2x + 1)(2 + 0) + \frac{150*-2{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{150({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{2}(x)} + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*9sin^{8}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x^{2}} + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)*-sin(2x + 1)(2 + 0)}{x^{2}} - \frac{1500*-{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{1500({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{1500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{1500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*2ln(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x(x)} - \frac{1500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)*13sin^{12}(2x + 1)cos(2x + 1)(2 + 0)cos^{2}(2x + 1)}{x} - \frac{1500{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)*-2cos(2x + 1)sin(2x + 1)(2 + 0)}{x} - \frac{150*-2{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{3}} - \frac{150({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{14}(2x + 1)cos(2x + 1)}{x^{2}(x)} - \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*14sin^{13}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x^{2}} - \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)*-sin(2x + 1)(2 + 0)}{x^{2}} + \frac{22500*-{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + \frac{22500({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} + \frac{22500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} + \frac{22500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*2ln(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x(x)} + \frac{22500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)*13sin^{12}(2x + 1)cos(2x + 1)(2 + 0)cos^{2}(2x + 1)}{x} + \frac{22500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)*-2cos(2x + 1)sin(2x + 1)(2 + 0)}{x} + \frac{2250*-2{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{2250({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{2250{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{2250{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{14}(2x + 1)cos(2x + 1)}{x^{2}(x)} + \frac{2250{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*14sin^{13}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x^{2}} + \frac{2250{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)*-sin(2x + 1)(2 + 0)}{x^{2}} - \frac{300*-2{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{3}} - \frac{300({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*9sin^{8}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x^{2}} - \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)*-sin(2x + 1)(2 + 0)}{x^{2}} - 125000({x}^{(3sin^{5}(2x + 1))}((3*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(3sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) - 125000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{3}(x)sin^{12}(2x + 1)cos^{3}(2x + 1) - \frac{125000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*3ln^{2}(x)sin^{12}(2x + 1)cos^{3}(2x + 1)}{(x)} - 125000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)*12sin^{11}(2x + 1)cos(2x + 1)(2 + 0)cos^{3}(2x + 1) - 125000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{12}(2x + 1)*-3cos^{2}(2x + 1)sin(2x + 1)(2 + 0) - \frac{37500*-{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{37500({x}^{(3sin^{5}(2x + 1))}((3*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(3sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{37500{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{37500{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*2ln(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x(x)} - \frac{37500{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)*13sin^{12}(2x + 1)cos(2x + 1)(2 + 0)cos^{2}(2x + 1)}{x} - \frac{37500{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)*-2cos(2x + 1)sin(2x + 1)(2 + 0)}{x} - \frac{750*-2{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{3}} - \frac{750({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{750{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{750{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{2}(x)} - \frac{750{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*9sin^{8}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x^{2}} - \frac{750{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)*-sin(2x + 1)(2 + 0)}{x^{2}} + 60000({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{7}(2x + 1)cos^{3}(2x + 1) + 60000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{2}(x)sin^{7}(2x + 1)cos^{3}(2x + 1) + \frac{60000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*2ln(x)sin^{7}(2x + 1)cos^{3}(2x + 1)}{(x)} + 60000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)*7sin^{6}(2x + 1)cos(2x + 1)(2 + 0)cos^{3}(2x + 1) + 60000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{7}(2x + 1)*-3cos^{2}(2x + 1)sin(2x + 1)(2 + 0) - 15000({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{9}(2x + 1)cos(2x + 1) - 15000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln^{2}(x)sin^{9}(2x + 1)cos(2x + 1) - \frac{15000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*2ln(x)sin^{9}(2x + 1)cos(2x + 1)}{(x)} - 15000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)*9sin^{8}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1) - 15000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{9}(2x + 1)*-sin(2x + 1)(2 + 0) - \frac{3750*-2{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{3}} - \frac{3750({x}^{(3sin^{5}(2x + 1))}((3*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(3sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{3750{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{2}} - \frac{3750{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{14}(2x + 1)cos(2x + 1)}{x^{2}(x)} - \frac{3750{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*14sin^{13}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x^{2}} - \frac{3750{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)*-sin(2x + 1)(2 + 0)}{x^{2}} + \frac{1500*-2{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{1500({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{9}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*9sin^{8}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x^{2}} + \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)*-sin(2x + 1)(2 + 0)}{x^{2}} - \frac{1500*-{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x^{2}} - \frac{1500({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x} - \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{10}(2x + 1)}{x} - \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x(x)} - \frac{1500{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*10sin^{9}(2x + 1)cos(2x + 1)(2 + 0)}{x} + \frac{150*-2{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{150({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{4}(2x + 1)cos(2x + 1)}{x^{2}} + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*4sin^{3}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1)}{x^{2}} + \frac{150{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)*-sin(2x + 1)(2 + 0)}{x^{2}} - \frac{1200*-{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{3}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{1200({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{3}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{1200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{3}(2x + 1)cos^{2}(2x + 1)}{x} - \frac{1200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*3sin^{2}(2x + 1)cos(2x + 1)(2 + 0)cos^{2}(2x + 1)}{x} - \frac{1200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{3}(2x + 1)*-2cos(2x + 1)sin(2x + 1)(2 + 0)}{x} + \frac{300*-{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{2}} + \frac{300({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x} + \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{5}(2x + 1)}{x} + \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0)}{x} - 2400({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{2}(2x + 1)cos^{3}(2x + 1) - 2400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{2}(2x + 1)cos^{3}(2x + 1) - \frac{2400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{2}(2x + 1)cos^{3}(2x + 1)}{(x)} - 2400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*2sin(2x + 1)cos(2x + 1)(2 + 0)cos^{3}(2x + 1) - 2400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{2}(2x + 1)*-3cos^{2}(2x + 1)sin(2x + 1)(2 + 0) + 2600({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{4}(2x + 1)cos(2x + 1) + 2600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{4}(2x + 1)cos(2x + 1) + \frac{2600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{(x)} + 2600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*4sin^{3}(2x + 1)cos(2x + 1)(2 + 0)cos(2x + 1) + 2600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{4}(2x + 1)*-sin(2x + 1)(2 + 0) + \frac{300*-{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x^{2}} + \frac{300({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x} + \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))ln(x)sin^{10}(2x + 1)}{x} + \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x(x)} + \frac{300{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)*10sin^{9}(2x + 1)cos(2x + 1)(2 + 0)}{x} - \frac{10*-3{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{4}} - \frac{10({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{3}} - \frac{10{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{5}(2x + 1)}{x^{3}} - \frac{10{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0)}{x^{3}} + \frac{15*-3{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{4}} + \frac{15({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{3}} + \frac{15{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{10}(2x + 1)}{x^{3}} + \frac{15{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*10sin^{9}(2x + 1)cos(2x + 1)(2 + 0)}{x^{3}} - \frac{75*-3{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{4}} - \frac{75({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{3}} - \frac{75{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{10}(2x + 1)}{x^{3}} - \frac{75{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*10sin^{9}(2x + 1)cos(2x + 1)(2 + 0)}{x^{3}} - \frac{5*-3{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{4}} - \frac{5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{3}} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{15}(2x + 1)}{x^{3}} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}*15sin^{14}(2x + 1)cos(2x + 1)(2 + 0)}{x^{3}} + \frac{75*-3{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{4}} + \frac{75({x}^{(2sin^{5}(2x + 1))}((2*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(2sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{3}} + \frac{75{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{15}(2x + 1)}{x^{3}} + \frac{75{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*15sin^{14}(2x + 1)cos(2x + 1)(2 + 0)}{x^{3}} - \frac{125*-3{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{4}} - \frac{125({x}^{(3sin^{5}(2x + 1))}((3*5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(3sin^{5}(2x + 1))(1)}{(x)}))e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{3}} - \frac{125{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*-5({x}^{sin^{5}(2x + 1)}((5sin^{4}(2x + 1)cos(2x + 1)(2 + 0))ln(x) + \frac{(sin^{5}(2x + 1))(1)}{(x)}))sin^{15}(2x + 1)}{x^{3}} - \frac{125{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}*15sin^{14}(2x + 1)cos(2x + 1)(2 + 0)}{x^{3}}\\=&-50000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{4}(x)sin^{16}(2x + 1)cos^{4}(2x + 1) - \frac{14400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + 1750000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{4}(x)sin^{16}(2x + 1)cos^{4}(2x + 1) + \frac{216000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{108000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{12}(2x + 1)cos^{3}(2x + 1)}{x} - 240000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{11}(2x + 1)cos^{4}(2x + 1) + 60000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{13}(2x + 1)cos^{2}(2x + 1) + \frac{8400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + \frac{1620000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{12}(2x + 1)cos^{3}(2x + 1)}{x} - \frac{10800{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{8}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{105600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{7}(2x + 1)cos^{3}(2x + 1)}{x} + \frac{34400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} - 7500000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{4}(x)sin^{16}(2x + 1)cos^{4}(2x + 1) - \frac{360000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + 3600000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{11}(2x + 1)cos^{4}(2x + 1) - 900000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{13}(2x + 1)cos^{2}(2x + 1) - \frac{42000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{8}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{2700000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{12}(2x + 1)cos^{3}(2x + 1)}{x} + \frac{54000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{8}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + \frac{528000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{7}(2x + 1)cos^{3}(2x + 1)}{x} - \frac{172000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x} - 192000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{6}(2x + 1)cos^{4}(2x + 1) + 152000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) + 1500000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{13}(2x + 1)cos^{2}(2x + 1) - \frac{400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{3000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + \frac{600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{3}} - \frac{45000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{9000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{1200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{12000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{14}(2x + 1)cos(2x + 1)}{x} - \frac{20000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{17}(2x + 1)cos^{3}(2x + 1)}{x} - \frac{3000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{18}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + \frac{700000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{17}(2x + 1)cos^{3}(2x + 1)}{x} + \frac{105000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{18}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{180000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{14}(2x + 1)cos(2x + 1)}{x} - \frac{200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{19}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{7000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{19}(2x + 1)cos(2x + 1)}{x^{3}} - \frac{600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{14}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{300000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{14}(2x + 1)cos(2x + 1)}{x} - \frac{3000000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{17}(2x + 1)cos^{3}(2x + 1)}{x} - \frac{450000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{18}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{30000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{19}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{9000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{14}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{75000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{13}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + \frac{10400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x} + 6250000{x}^{(4sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{4}(x)sin^{16}(2x + 1)cos^{4}(2x + 1) + \frac{2500000{x}^{(4sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{17}(2x + 1)cos^{3}(2x + 1)}{x} - 6000000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{3}(x)sin^{11}(2x + 1)cos^{4}(2x + 1) - 760000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{8}(2x + 1)cos^{2}(2x + 1) + \frac{2000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{9}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{375000{x}^{(4sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{18}(2x + 1)cos^{2}(2x + 1)}{x^{2}} + \frac{15000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{14}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{25000{x}^{(4sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{19}(2x + 1)cos(2x + 1)}{x^{3}} - \frac{6000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{9}(2x + 1)cos(2x + 1)}{x^{3}} + 960000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{6}(2x + 1)cos^{4}(2x + 1) + 35200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{3}(2x + 1)cos^{2}(2x + 1) - 9600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin(2x + 1)cos^{4}(2x + 1) + \frac{600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{15}(2x + 1)}{x^{2}} - \frac{15000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{14}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{15000{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{15}(2x + 1)}{x^{2}} - \frac{400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{4}(2x + 1)cos(2x + 1)}{x^{3}} + \frac{2400{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{3}(2x + 1)cos^{2}(2x + 1)}{x^{2}} - \frac{9600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{2}(2x + 1)cos^{3}(2x + 1)}{x} - \frac{9000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{15}(2x + 1)}{x^{2}} - \frac{600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{2}} - \frac{6000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{2}} + \frac{1200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{2}} + \frac{3000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x^{2}} - 6000{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{10}(2x + 1) + 30000{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}ln^{2}(x)sin^{10}(2x + 1) - 5200{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{5}(2x + 1) + \frac{30{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{5}(2x + 1)}{x^{4}} - \frac{55{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{4}} - \frac{600{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}ln(x)sin^{10}(2x + 1)}{x^{2}} + \frac{275{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{10}(2x + 1)}{x^{4}} + \frac{30{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{4}} - \frac{450{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{4}} + \frac{750{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{15}(2x + 1)}{x^{4}} - \frac{5{x}^{sin^{5}(2x + 1)}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{20}(2x + 1)}{x^{4}} + \frac{175{x}^{(2sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{20}(2x + 1)}{x^{4}} - \frac{750{x}^{(3sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{20}(2x + 1)}{x^{4}} + \frac{625{x}^{(4sin^{5}(2x + 1))}e^{-5{x}^{sin^{5}(2x + 1)}}sin^{20}(2x + 1)}{x^{4}}\\ \end{split}\end{equation} \]