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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {sin({x}^{2} + x)}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {sin(x^{2} + x)}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {sin(x^{2} + x)}^{x}\right)}{dx}\\=&({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))\\=&{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) + \frac{2x^{2}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{x{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) + \frac{2x^{2}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{x{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)}\right)}{dx}\\=&({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x)) + \frac{{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)}{(sin(x^{2} + x))} + \frac{2*2x{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x^{2}{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{2x^{2}{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{x{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{x{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)}\\=&{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x)) + \frac{4x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{4x^{4}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{3x^{2}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{x{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - 4x^{2}{sin(x^{2} + x)}^{x} - 4x^{3}{sin(x^{2} + x)}^{x} - x{sin(x^{2} + x)}^{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x)) + \frac{4x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{4x^{4}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{3x^{2}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{x{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - 4x^{2}{sin(x^{2} + x)}^{x} - 4x^{3}{sin(x^{2} + x)}^{x} - x{sin(x^{2} + x)}^{x}\right)}{dx}\\=&({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln^{2}(sin(x^{2} + x)) + \frac{{sin(x^{2} + x)}^{x}*2ln(sin(x^{2} + x))cos(x^{2} + x)(2x + 1)}{(sin(x^{2} + x))} + \frac{4*2x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{4x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{4x^{2}{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{(sin(x^{2} + x))sin(x^{2} + x)} + \frac{4x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{4x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{2{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{(sin(x^{2} + x))sin(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{6{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{6x{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{2({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{2{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{4*4x^{3}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{4x^{4}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{4x^{4}{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{4x^{4}{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} - \frac{3*2x{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{3x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{3x^{2}{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{3x^{2}{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} - \frac{{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{x{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{x{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} - 4*2x{sin(x^{2} + x)}^{x} - 4x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))})) - 4*3x^{2}{sin(x^{2} + x)}^{x} - 4x^{3}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))})) - {sin(x^{2} + x)}^{x} - x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))\\=&\frac{6{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x^{2}{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{3x{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{18x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + {sin(x^{2} + x)}^{x}ln^{3}(sin(x^{2} + x)) + \frac{12x^{4}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{36x^{3}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{6x^{2}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{9x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{3x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - 12x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) - \frac{12x{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - 12x^{3}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) - 3x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) + \frac{6{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{24x^{5}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{20x^{4}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{3{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{12x^{5}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - 3{sin(x^{2} + x)}^{x} + \frac{8x^{6}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{14x^{4}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{6x^{3}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{9x^{2}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{7x^{3}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{9x^{2}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - 18x{sin(x^{2} + x)}^{x} - 24x^{2}{sin(x^{2} + x)}^{x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x^{2}{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{3x{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{18x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + {sin(x^{2} + x)}^{x}ln^{3}(sin(x^{2} + x)) + \frac{12x^{4}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{36x^{3}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{6x^{2}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{9x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{3x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - 12x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) - \frac{12x{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - 12x^{3}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) - 3x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) + \frac{6{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{24x^{5}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{20x^{4}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{3{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{12x^{5}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - 3{sin(x^{2} + x)}^{x} + \frac{8x^{6}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{14x^{4}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{6x^{3}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{9x^{2}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{7x^{3}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{9x^{2}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - 18x{sin(x^{2} + x)}^{x} - 24x^{2}{sin(x^{2} + x)}^{x}\right)}{dx}\\=&\frac{6({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{(sin(x^{2} + x))sin(x^{2} + x)} + \frac{6{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{6{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{6*2x{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x^{2}{sin(x^{2} + x)}^{x}*2ln(sin(x^{2} + x))cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{(sin(x^{2} + x))sin(x^{2} + x)} + \frac{6x^{2}{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{6x^{2}{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{3{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{3x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{3x{sin(x^{2} + x)}^{x}*2ln(sin(x^{2} + x))cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{(sin(x^{2} + x))sin(x^{2} + x)} + \frac{3x{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{3x{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{18{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{18x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{18x{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{(sin(x^{2} + x))sin(x^{2} + x)} + \frac{18x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{18x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + ({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln^{3}(sin(x^{2} + x)) + \frac{{sin(x^{2} + x)}^{x}*3ln^{2}(sin(x^{2} + x))cos(x^{2} + x)(2x + 1)}{(sin(x^{2} + x))} + \frac{12*4x^{3}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{12x^{4}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{12x^{4}{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{(sin(x^{2} + x))sin^{2}(x^{2} + x)} + \frac{12x^{4}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{12x^{4}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} + \frac{36*3x^{2}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{36x^{3}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{36x^{3}{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{36x^{3}{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} + \frac{6*2x{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{6x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{6x^{2}{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{6x^{2}{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} - \frac{9*2x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{9x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{9x^{2}{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{(sin(x^{2} + x))sin^{2}(x^{2} + x)} - \frac{9x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{9x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} - \frac{3{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{3x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{3x{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{(sin(x^{2} + x))sin^{2}(x^{2} + x)} - \frac{3x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{3x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} - 12*2x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) - 12x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x)) - \frac{12x^{2}{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)}{(sin(x^{2} + x))} - \frac{12{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{12x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{12x{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{12x{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} - 12*3x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) - 12x^{3}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x)) - \frac{12x^{3}{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)}{(sin(x^{2} + x))} - 3{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) - 3x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))ln(sin(x^{2} + x)) - \frac{3x{sin(x^{2} + x)}^{x}cos(x^{2} + x)(2x + 1)}{(sin(x^{2} + x))} + \frac{6({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{6{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} - \frac{24*5x^{4}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{24x^{5}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{24x^{5}{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{24x^{5}{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} - \frac{20*4x^{3}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{20x^{4}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{20x^{4}{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{20x^{4}{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} - \frac{3({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{3{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)(2x + 1)cos^{2}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{3{sin(x^{2} + x)}^{x}*-2cos(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{2}(x^{2} + x)} - \frac{12*5x^{4}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{12x^{5}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{12x^{5}{sin(x^{2} + x)}^{x}*-3cos(x^{2} + x)(2x + 1)cos^{3}(x^{2} + x)}{sin^{4}(x^{2} + x)} - \frac{12x^{5}{sin(x^{2} + x)}^{x}*-3cos^{2}(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{3}(x^{2} + x)} - 3({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))})) + \frac{8*6x^{5}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{8x^{6}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{8x^{6}{sin(x^{2} + x)}^{x}*-3cos(x^{2} + x)(2x + 1)cos^{3}(x^{2} + x)}{sin^{4}(x^{2} + x)} + \frac{8x^{6}{sin(x^{2} + x)}^{x}*-3cos^{2}(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{3}(x^{2} + x)} - \frac{14*4x^{3}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{14x^{4}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{14x^{4}{sin(x^{2} + x)}^{x}*-3cos(x^{2} + x)(2x + 1)cos^{3}(x^{2} + x)}{sin^{4}(x^{2} + x)} - \frac{14x^{4}{sin(x^{2} + x)}^{x}*-3cos^{2}(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{3}(x^{2} + x)} + \frac{6*3x^{2}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x^{3}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{6x^{3}{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{6x^{3}{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{9*2x{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{9x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{9x^{2}{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{9x^{2}{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{7*3x^{2}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{7x^{3}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{7x^{3}{sin(x^{2} + x)}^{x}*-3cos(x^{2} + x)(2x + 1)cos^{3}(x^{2} + x)}{sin^{4}(x^{2} + x)} + \frac{7x^{3}{sin(x^{2} + x)}^{x}*-3cos^{2}(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{3}(x^{2} + x)} + \frac{9*2x{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{9x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{9x^{2}{sin(x^{2} + x)}^{x}*-3cos(x^{2} + x)(2x + 1)cos^{3}(x^{2} + x)}{sin^{4}(x^{2} + x)} + \frac{9x^{2}{sin(x^{2} + x)}^{x}*-3cos^{2}(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{3}(x^{2} + x)} + \frac{2{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}*-cos(x^{2} + x)(2x + 1)cos(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}*-sin(x^{2} + x)(2x + 1)}{sin(x^{2} + x)} + \frac{2{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{2x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}*-3cos(x^{2} + x)(2x + 1)cos^{3}(x^{2} + x)}{sin^{4}(x^{2} + x)} + \frac{2x{sin(x^{2} + x)}^{x}*-3cos^{2}(x^{2} + x)sin(x^{2} + x)(2x + 1)}{sin^{3}(x^{2} + x)} - 18{sin(x^{2} + x)}^{x} - 18x({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))})) - 24*2x{sin(x^{2} + x)}^{x} - 24x^{2}({sin(x^{2} + x)}^{x}((1)ln(sin(x^{2} + x)) + \frac{(x)(cos(x^{2} + x)(2x + 1))}{(sin(x^{2} + x))}))\\=&\frac{12{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{24x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{48x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{28x{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{12{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{12{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{36x{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{144x^{3}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{8x^{2}{sin(x^{2} + x)}^{x}ln^{3}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{24x^{4}{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{18x^{2}{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{96x^{5}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{80x^{4}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{6x{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x))cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{24{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{4x{sin(x^{2} + x)}^{x}ln^{3}(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{24x^{3}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{36x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{8x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos(x^{2} + x)}{sin(x^{2} + x)} - 12{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) + \frac{106x^{2}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{48x^{5}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + {sin(x^{2} + x)}^{x}ln^{4}(sin(x^{2} + x)) + \frac{32x^{6}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{144x^{5}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{144x^{4}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{56x^{4}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{28x^{3}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{36x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{8x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x))cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{188x^{3}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - \frac{336x^{4}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{272x^{3}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{24x^{2}{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{12x^{2}{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - 72x{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) - 24x^{3}{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x)) - 6x{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x)) + \frac{48x{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} - 24x^{2}{sin(x^{2} + x)}^{x}ln^{2}(sin(x^{2} + x)) - 96x^{2}{sin(x^{2} + x)}^{x}ln(sin(x^{2} + x)) + \frac{48x{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} + \frac{8{sin(x^{2} + x)}^{x}cos(x^{2} + x)}{sin(x^{2} + x)} - \frac{96x^{7}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{32x^{6}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{176x^{5}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{32x^{4}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} + \frac{8{sin(x^{2} + x)}^{x}cos^{3}(x^{2} + x)}{sin^{3}(x^{2} + x)} + \frac{8x^{6}{sin(x^{2} + x)}^{x}cos^{4}(x^{2} + x)}{sin^{4}(x^{2} + x)} - 24{sin(x^{2} + x)}^{x} - \frac{64x^{7}{sin(x^{2} + x)}^{x}cos^{4}(x^{2} + x)}{sin^{4}(x^{2} + x)} + \frac{120x^{5}{sin(x^{2} + x)}^{x}cos^{4}(x^{2} + x)}{sin^{4}(x^{2} + x)} + \frac{16x^{8}{sin(x^{2} + x)}^{x}cos^{4}(x^{2} + x)}{sin^{4}(x^{2} + x)} - \frac{86x^{3}{sin(x^{2} + x)}^{x}cos^{2}(x^{2} + x)}{sin^{2}(x^{2} + x)} - \frac{62x^{3}{sin(x^{2} + x)}^{x}cos^{4}(x^{2} + x)}{sin^{4}(x^{2} + x)} - \frac{37x^{2}{sin(x^{2} + x)}^{x}cos^{4}(x^{2} + x)}{sin^{4}(x^{2} + x)} - \frac{6x{sin(x^{2} + x)}^{x}cos^{4}(x^{2} + x)}{sin^{4}(x^{2} + x)} + \frac{25x^{4}{sin(x^{2} + x)}^{x}cos^{4}(x^{2} + x)}{sin^{4}(x^{2} + x)} - 62x{sin(x^{2} + x)}^{x} + 64x^{5}{sin(x^{2} + x)}^{x} + 8x^{4}{sin(x^{2} + x)}^{x} - 24x^{3}{sin(x^{2} + x)}^{x} + 48x^{6}{sin(x^{2} + x)}^{x} - 13x^{2}{sin(x^{2} + x)}^{x}\\ \end{split}\end{equation} \]