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 15 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ {x}^{(1 - ln(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {x}^{(-ln(x) + 1)}\\\\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&\frac{-34690583328{x}^{(-ln(x) + 1)}ln^{2}(x)ln(x)}{x^{15}} - \frac{110807959080{x}^{(-ln(x) + 1)}ln^{3}(x)ln(x)}{x^{15}} - \frac{136808233380{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{2}(x)}{x^{15}} - \frac{66005854460{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{3}(x)}{x^{15}} + \frac{121084787160{x}^{(-ln(x) + 1)}ln(x)ln(x)}{x^{15}} - \frac{36131800250{x}^{(-ln(x) + 1)}ln^{4}(x)ln(x)}{x^{15}} - \frac{69134727480{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{2}(x)}{x^{15}} + \frac{10497587100{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{3}(x)}{x^{15}} - \frac{7958672604{x}^{(-ln(x) + 1)}ln(x)ln^{2}(x)}{x^{15}} - \frac{7958672604{x}^{(-ln(x) + 1)}ln(x)ln^{2}(x)}{x^{15}} - \frac{69134727480{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{2}(x)}{x^{15}} - \frac{34690583328{x}^{(-ln(x) + 1)}ln^{2}(x)ln(x)}{x^{15}} + \frac{1373121750{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{4}(x)}{x^{15}} - \frac{71603018760{x}^{(-ln(x) + 1)}ln(x)ln^{3}(x)}{x^{15}} - \frac{136808233380{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{2}(x)}{x^{15}} + \frac{14373258900{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{2}(x)}{x^{15}} + \frac{14373258900{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{2}(x)}{x^{15}} + \frac{24150666540{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{3}(x)}{x^{15}} - \frac{110807959080{x}^{(-ln(x) + 1)}ln^{3}(x)ln(x)}{x^{15}} - \frac{71603018760{x}^{(-ln(x) + 1)}ln(x)ln^{3}(x)}{x^{15}} - \frac{66005854460{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{3}(x)}{x^{15}} + \frac{8349330990{x}^{(-ln(x) + 1)}ln^{5}(x)ln(x)}{x^{15}} + \frac{121084787160{x}^{(-ln(x) + 1)}ln(x)ln(x)}{x^{15}} + \frac{10497587100{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{3}(x)}{x^{15}} + \frac{19171657505{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{4}(x)}{x^{15}} + \frac{24150666540{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{3}(x)}{x^{15}} - \frac{31438490720{x}^{(-ln(x) + 1)}ln(x)ln^{4}(x)}{x^{15}} + \frac{17477805345{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{2}(x)}{x^{15}} + \frac{7079992920{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{3}(x)}{x^{15}} - \frac{36131800250{x}^{(-ln(x) + 1)}ln^{4}(x)ln(x)}{x^{15}} - \frac{31438490720{x}^{(-ln(x) + 1)}ln(x)ln^{4}(x)}{x^{15}} + \frac{8515589082{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{5}(x)}{x^{15}} + \frac{1373121750{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{4}(x)}{x^{15}} + \frac{17477805345{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{2}(x)}{x^{15}} + \frac{7881073200{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{4}(x)}{x^{15}} + \frac{3927563640{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{2}(x)}{x^{15}} - \frac{78398320{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{3}(x)}{x^{15}} + \frac{8349330990{x}^{(-ln(x) + 1)}ln^{5}(x)ln(x)}{x^{15}} + \frac{5529724200{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{5}(x)}{x^{15}} + \frac{19171657505{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{4}(x)}{x^{15}} + \frac{7881073200{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{4}(x)}{x^{15}} + \frac{94134040{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{4}(x)}{x^{15}} - \frac{94094000{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{2}(x)}{x^{15}} - \frac{2050778730{x}^{(-ln(x) + 1)}ln(x)ln^{5}(x)}{x^{15}} - \frac{437271120{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{3}(x)}{x^{15}} + \frac{6821736922{x}^{(-ln(x) + 1)}ln^{6}(x)ln(x)}{x^{15}} + \frac{305865560{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{5}(x)}{x^{15}} - \frac{631711080{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{4}(x)}{x^{15}} + \frac{8515589082{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{5}(x)}{x^{15}} + \frac{6821736922{x}^{(-ln(x) + 1)}ln^{6}(x)ln(x)}{x^{15}} - \frac{192586680{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{2}(x)}{x^{15}} - \frac{102942840{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{3}(x)}{x^{15}} + \frac{1232894520{x}^{(-ln(x) + 1)}ln^{7}(x)ln(x)}{x^{15}} - \frac{597837240{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{5}(x)}{x^{15}} - \frac{178438260{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{4}(x)}{x^{15}} - \frac{2050778730{x}^{(-ln(x) + 1)}ln(x)ln^{5}(x)}{x^{15}} + \frac{7079992920{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{3}(x)}{x^{15}} + \frac{2377294920{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{6}(x)}{x^{15}} - \frac{38888850{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{2}(x)}{x^{15}} - \frac{11840400{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{3}(x)}{x^{15}} - \frac{38647180{x}^{(-ln(x) + 1)}ln^{8}(x)ln(x)}{x^{15}} - \frac{211387176{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{5}(x)}{x^{15}} + \frac{5529724200{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{5}(x)}{x^{15}} - \frac{23616450{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{4}(x)}{x^{15}} + \frac{305865560{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{5}(x)}{x^{15}} + \frac{345064720{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{6}(x)}{x^{15}} + \frac{1842727887{x}^{(-ln(x) + 1)}ln(x)ln^{6}(x)}{x^{15}} - \frac{3955380{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{2}(x)}{x^{15}} - \frac{756756{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{3}(x)}{x^{15}} + \frac{2377294920{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{6}(x)}{x^{15}} - \frac{49154820{x}^{(-ln(x) + 1)}ln^{9}(x)ln(x)}{x^{15}} - \frac{32947200{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{5}(x)}{x^{15}} + \frac{3927563640{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{2}(x)}{x^{15}} - \frac{1701700{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{4}(x)}{x^{15}} - \frac{364684320{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{6}(x)}{x^{15}} - \frac{227136{x}^{(-ln(x) + 1)}ln^{11}(x)ln^{2}(x)}{x^{15}} + \frac{94134040{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{4}(x)}{x^{15}} - \frac{25740{x}^{(-ln(x) + 1)}ln^{11}(x)ln^{3}(x)}{x^{15}} + \frac{345064720{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{6}(x)}{x^{15}} - \frac{8692684{x}^{(-ln(x) + 1)}ln^{10}(x)ln(x)}{x^{15}} - \frac{2720718{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{5}(x)}{x^{15}} + \frac{568493640{x}^{(-ln(x) + 1)}ln(x)ln^{7}(x)}{x^{15}} - \frac{364684320{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{6}(x)}{x^{15}} - \frac{64350{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{4}(x)}{x^{15}} + \frac{208379600{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{7}(x)}{x^{15}} - \frac{172960788{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{6}(x)}{x^{15}} - \frac{7020{x}^{(-ln(x) + 1)}ln^{12}(x)ln^{2}(x)}{x^{15}} - \frac{78398320{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{3}(x)}{x^{15}} - \frac{364{x}^{(-ln(x) + 1)}ln^{12}(x)ln^{3}(x)}{x^{15}} - \frac{792480{x}^{(-ln(x) + 1)}ln^{11}(x)ln(x)}{x^{15}} - \frac{115830{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{5}(x)}{x^{15}} - \frac{597837240{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{5}(x)}{x^{15}} - \frac{1001{x}^{(-ln(x) + 1)}ln^{11}(x)ln^{4}(x)}{x^{15}} + \frac{67218580{x}^{(-ln(x) + 1)}ln(x)ln^{8}(x)}{x^{15}} - \frac{132097680{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{7}(x)}{x^{15}} - \frac{32792760{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{6}(x)}{x^{15}} - \frac{91{x}^{(-ln(x) + 1)}ln^{13}(x)ln^{2}(x)}{x^{15}} - \frac{20926620{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{8}(x)}{x^{15}} - \frac{96096000{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{7}(x)}{x^{15}} - \frac{14{x}^{(-ln(x) + 1)}ln^{14}(x)ln(x)}{x^{15}} - \frac{41314{x}^{(-ln(x) + 1)}ln^{12}(x)ln(x)}{x^{15}} - \frac{1170{x}^{(-ln(x) + 1)}ln^{13}(x)ln(x)}{x^{15}} - \frac{631711080{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{4}(x)}{x^{15}} - \frac{2002{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{5}(x)}{x^{15}} - \frac{172960788{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{6}(x)}{x^{15}} - \frac{3171168{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{6}(x)}{x^{15}} - \frac{3003{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{6}(x)}{x^{15}} + \frac{1232894520{x}^{(-ln(x) + 1)}ln^{7}(x)ln(x)}{x^{15}} - \frac{154440{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{6}(x)}{x^{15}} + \frac{1842727887{x}^{(-ln(x) + 1)}ln(x)ln^{6}(x)}{x^{15}} - \frac{34324290{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{8}(x)}{x^{15}} - \frac{3432{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{7}(x)}{x^{15}} - \frac{154440{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{7}(x)}{x^{15}} + \frac{1707420{x}^{(-ln(x) + 1)}ln(x)ln^{9}(x)}{x^{15}} - \frac{11518650{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{8}(x)}{x^{15}} - \frac{6866860{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{9}(x)}{x^{15}} - \frac{3003{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{8}(x)}{x^{15}} - \frac{2714712{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{7}(x)}{x^{15}} - \frac{211387176{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{5}(x)}{x^{15}} + \frac{208379600{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{7}(x)}{x^{15}} - \frac{115830{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{8}(x)}{x^{15}} - \frac{23268960{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{7}(x)}{x^{15}} - \frac{2002{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{9}(x)}{x^{15}} - \frac{23268960{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{7}(x)}{x^{15}} - \frac{458458{x}^{(-ln(x) + 1)}ln(x)ln^{10}(x)}{x^{15}} - \frac{94094000{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{2}(x)}{x^{15}} - \frac{1693692{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{8}(x)}{x^{15}} - \frac{729300{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{10}(x)}{x^{15}} - \frac{3775200{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{9}(x)}{x^{15}} - \frac{132097680{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{7}(x)}{x^{15}} - \frac{96096000{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{7}(x)}{x^{15}} - \frac{750750{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{9}(x)}{x^{15}} - \frac{64350{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{9}(x)}{x^{15}} - \frac{1001{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{10}(x)}{x^{15}} - \frac{32792760{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{6}(x)}{x^{15}} - \frac{1693692{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{8}(x)}{x^{15}} - \frac{11518650{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{8}(x)}{x^{15}} - \frac{750750{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{9}(x)}{x^{15}} - \frac{59280{x}^{(-ln(x) + 1)}ln(x)ln^{11}(x)}{x^{15}} - \frac{437271120{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{3}(x)}{x^{15}} - \frac{25740{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{10}(x)}{x^{15}} - \frac{364{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{11}(x)}{x^{15}} - \frac{224224{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{10}(x)}{x^{15}} - \frac{40404{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{11}(x)}{x^{15}} - \frac{25740{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{10}(x)}{x^{15}} - \frac{34324290{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{8}(x)}{x^{15}} - \frac{3775200{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{9}(x)}{x^{15}} - \frac{224224{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{10}(x)}{x^{15}} - \frac{2714712{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{7}(x)}{x^{15}} - \frac{7020{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{11}(x)}{x^{15}} - \frac{91{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{12}(x)}{x^{15}} - \frac{64350{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{9}(x)}{x^{15}} - \frac{3276{x}^{(-ln(x) + 1)}ln(x)ln^{12}(x)}{x^{15}} - \frac{178438260{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{4}(x)}{x^{15}} - \frac{7020{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{11}(x)}{x^{15}} - \frac{364{x}^{(-ln(x) + 1)}ln^{4}(x)ln^{11}(x)}{x^{15}} - \frac{20926620{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{8}(x)}{x^{15}} - \frac{115830{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{8}(x)}{x^{15}} - \frac{6866860{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{9}(x)}{x^{15}} - \frac{729300{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{10}(x)}{x^{15}} - \frac{1001{x}^{(-ln(x) + 1)}ln^{5}(x)ln^{10}(x)}{x^{15}} - \frac{40404{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{11}(x)}{x^{15}} - \frac{32947200{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{5}(x)}{x^{15}} - \frac{91{x}^{(-ln(x) + 1)}ln^{3}(x)ln^{12}(x)}{x^{15}} - \frac{1170{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{12}(x)}{x^{15}} - \frac{14{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{13}(x)}{x^{15}} - \frac{3171168{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{6}(x)}{x^{15}} - \frac{14{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{13}(x)}{x^{15}} - \frac{1170{x}^{(-ln(x) + 1)}ln^{2}(x)ln^{12}(x)}{x^{15}} - \frac{2002{x}^{(-ln(x) + 1)}ln^{6}(x)ln^{9}(x)}{x^{15}} - \frac{3003{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{8}(x)}{x^{15}} - \frac{2720718{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{5}(x)}{x^{15}} - \frac{154440{x}^{(-ln(x) + 1)}ln^{7}(x)ln^{7}(x)}{x^{15}} - \frac{3432{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{7}(x)}{x^{15}} + \frac{568493640{x}^{(-ln(x) + 1)}ln(x)ln^{7}(x)}{x^{15}} - \frac{154440{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{6}(x)}{x^{15}} - \frac{23616450{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{4}(x)}{x^{15}} - \frac{3003{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{6}(x)}{x^{15}} - \frac{1701700{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{4}(x)}{x^{15}} - \frac{38647180{x}^{(-ln(x) + 1)}ln^{8}(x)ln(x)}{x^{15}} - \frac{102942840{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{3}(x)}{x^{15}} - \frac{115830{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{5}(x)}{x^{15}} - \frac{11840400{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{3}(x)}{x^{15}} - \frac{2002{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{5}(x)}{x^{15}} - \frac{756756{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{3}(x)}{x^{15}} + \frac{67218580{x}^{(-ln(x) + 1)}ln(x)ln^{8}(x)}{x^{15}} + \frac{1707420{x}^{(-ln(x) + 1)}ln(x)ln^{9}(x)}{x^{15}} - \frac{192586680{x}^{(-ln(x) + 1)}ln^{8}(x)ln^{2}(x)}{x^{15}} - \frac{458458{x}^{(-ln(x) + 1)}ln(x)ln^{10}(x)}{x^{15}} - \frac{64350{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{4}(x)}{x^{15}} - \frac{38888850{x}^{(-ln(x) + 1)}ln^{9}(x)ln^{2}(x)}{x^{15}} - \frac{59280{x}^{(-ln(x) + 1)}ln(x)ln^{11}(x)}{x^{15}} - \frac{1001{x}^{(-ln(x) + 1)}ln^{11}(x)ln^{4}(x)}{x^{15}} - \frac{3955380{x}^{(-ln(x) + 1)}ln^{10}(x)ln^{2}(x)}{x^{15}} - \frac{3276{x}^{(-ln(x) + 1)}ln(x)ln^{12}(x)}{x^{15}} - \frac{227136{x}^{(-ln(x) + 1)}ln^{11}(x)ln^{2}(x)}{x^{15}} - \frac{25740{x}^{(-ln(x) + 1)}ln^{11}(x)ln^{3}(x)}{x^{15}} - \frac{364{x}^{(-ln(x) + 1)}ln^{12}(x)ln^{3}(x)}{x^{15}} - \frac{49154820{x}^{(-ln(x) + 1)}ln^{9}(x)ln(x)}{x^{15}} - \frac{8692684{x}^{(-ln(x) + 1)}ln^{10}(x)ln(x)}{x^{15}} - \frac{792480{x}^{(-ln(x) + 1)}ln^{11}(x)ln(x)}{x^{15}} - \frac{41314{x}^{(-ln(x) + 1)}ln^{12}(x)ln(x)}{x^{15}} - \frac{7020{x}^{(-ln(x) + 1)}ln^{12}(x)ln^{2}(x)}{x^{15}} - \frac{1170{x}^{(-ln(x) + 1)}ln^{13}(x)ln(x)}{x^{15}} - \frac{90{x}^{(-ln(x) + 1)}ln(x)ln^{13}(x)}{x^{15}} - \frac{90{x}^{(-ln(x) + 1)}ln(x)ln^{13}(x)}{x^{15}} - \frac{91{x}^{(-ln(x) + 1)}ln^{13}(x)ln^{2}(x)}{x^{15}} - \frac{14{x}^{(-ln(x) + 1)}ln^{14}(x)ln(x)}{x^{15}} - \frac{{x}^{(-ln(x) + 1)}ln(x)ln^{14}(x)}{x^{15}} - \frac{{x}^{(-ln(x) + 1)}ln(x)ln^{14}(x)}{x^{15}} - \frac{70980{x}^{(-ln(x) + 1)}ln^{12}(x)}{x^{15}} + \frac{121288123704{x}^{(-ln(x) + 1)}ln(x)}{x^{15}} + \frac{1237780687{x}^{(-ln(x) + 1)}ln^{7}(x)}{x^{15}} + \frac{121288123704{x}^{(-ln(x) + 1)}ln(x)}{x^{15}} + \frac{1049758710{x}^{(-ln(x) + 1)}ln^{6}(x)}{x^{15}} - \frac{4744740{x}^{(-ln(x) + 1)}ln^{10}(x)}{x^{15}} + \frac{225173520{x}^{(-ln(x) + 1)}ln^{8}(x)}{x^{15}} + \frac{3174600{x}^{(-ln(x) + 1)}ln^{9}(x)}{x^{15}} + \frac{121084787160{x}^{(-ln(x) + 1)}ln^{2}(x)}{x^{15}} - \frac{4744740{x}^{(-ln(x) + 1)}ln^{10}(x)}{x^{15}} - \frac{14216418644{x}^{(-ln(x) + 1)}ln^{3}(x)}{x^{15}} + \frac{3174600{x}^{(-ln(x) + 1)}ln^{9}(x)}{x^{15}} - \frac{831922{x}^{(-ln(x) + 1)}ln^{11}(x)}{x^{15}} + \frac{121084787160{x}^{(-ln(x) + 1)}ln^{2}(x)}{x^{15}} - \frac{13514058194{x}^{(-ln(x) + 1)}ln^{5}(x)}{x^{15}} - \frac{45602744460{x}^{(-ln(x) + 1)}ln^{4}(x)}{x^{15}} + \frac{225173520{x}^{(-ln(x) + 1)}ln^{8}(x)}{x^{15}} - \frac{70980{x}^{(-ln(x) + 1)}ln^{12}(x)}{x^{15}} + \frac{1237780687{x}^{(-ln(x) + 1)}ln^{7}(x)}{x^{15}} - \frac{45602744460{x}^{(-ln(x) + 1)}ln^{4}(x)}{x^{15}} - \frac{14216418644{x}^{(-ln(x) + 1)}ln^{3}(x)}{x^{15}} - \frac{3430{x}^{(-ln(x) + 1)}ln^{13}(x)}{x^{15}} + \frac{1049758710{x}^{(-ln(x) + 1)}ln^{6}(x)}{x^{15}} - \frac{13514058194{x}^{(-ln(x) + 1)}ln^{5}(x)}{x^{15}} - \frac{90{x}^{(-ln(x) + 1)}ln^{14}(x)}{x^{15}} - \frac{{x}^{(-ln(x) + 1)}ln^{15}(x)}{x^{15}} - \frac{3430{x}^{(-ln(x) + 1)}ln^{13}(x)}{x^{15}} - \frac{90{x}^{(-ln(x) + 1)}ln^{14}(x)}{x^{15}} - \frac{831922{x}^{(-ln(x) + 1)}ln^{11}(x)}{x^{15}} - \frac{{x}^{(-ln(x) + 1)}ln^{15}(x)}{x^{15}} - \frac{6939932400{x}^{(-ln(x) + 1)}}{x^{15}}\\ \end{split}\end{equation} \]