Производная (x+2*log(5*x^2))^(atan(7*x^3-1)/sin(9*x))+e^175/pi

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↑ Функция f () ? - производная -го порядка

Решение

Вы ввели
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                     /   3    \       
                 atan\7*x  - 1/       
                 --------------       
                    sin(9*x)       175
/         /   2\\                 E   
\x + 2*log\5*x //               + ----
                                   pi 
$$\left(x + 2 \log{\left (5 x^{2} \right )}\right)^{\frac{\operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}}} + \frac{e^{175}}{\pi}$$
Подробное решение
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  1. дифференцируем почленно:

    1. Не могу найти шаги в поиске этой производной.

      Но производная

    2. Производная постоянной равна нулю.

    В результате:

  2. Теперь упростим:


Ответ:

График
Первая производная
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                     /   3    \                                                                                                               
                 atan\7*x  - 1/                                                                                                               
                 -------------- /                                                                                    /    4\     /   3    \  \
                    sin(9*x)    |/        /   3    \                          2           \                          |1 + -|*atan\7*x  - 1/  |
/         /   2\\               ||  9*atan\7*x  - 1/*cos(9*x)             21*x            |    /         /   2\\     \    x/                 |
\x + 2*log\5*x //              *||- ------------------------- + --------------------------|*log\x + 2*log\5*x // + --------------------------|
                                ||             2                /              2\         |                        /         /   2\\         |
                                ||          sin (9*x)           |    /   3    \ |         |                        \x + 2*log\5*x //*sin(9*x)|
                                \\                              \1 + \7*x  - 1/ /*sin(9*x)/                                                  /
$$\left(x + 2 \log{\left (5 x^{2} \right )}\right)^{\frac{\operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}}} \left(\frac{\left(1 + \frac{4}{x}\right) \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \sin{\left (9 x \right )}} + \left(\frac{21 x^{2}}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right) \sin{\left (9 x \right )}} - \frac{9 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin^{2}{\left (9 x \right )}} \cos{\left (9 x \right )}\right) \log{\left (x + 2 \log{\left (5 x^{2} \right )} \right )}\right)$$
Вторая производная
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                                 /                                                                                                  2                                                                                                                                                                                                                                                                                                                                              \
                                 |/                                                                         /    4\     /        3\\                                                                                                                                                                                                                                                                                                                                               |
                                 ||  /         2               /        3\         \                        |1 + -|*atan\-1 + 7*x /|                                                                                                                                                                                                                    /         2               /        3\         \                                                                            |
                     /        3\ ||  |      7*x          3*atan\-1 + 7*x /*cos(9*x)|    /         /   2\\   \    x/                |                                                                                                                                                                                                            /    4\ |      7*x          3*atan\-1 + 7*x /*cos(9*x)|                                                                            |
                 atan\-1 + 7*x / ||3*|---------------- - --------------------------|*log\x + 2*log\5*x // + -----------------------|                                                                                                                                                               2                                          3*|1 + -|*|---------------- - --------------------------|                                                                            |
                 --------------- ||  |               2            sin(9*x)         |                                     /   2\    |                                                                                                                                                        /    4\      /        3\                            \    x/ |               2            sin(9*x)         |                  2 /    4\                 /    4\     /        3\         |
                     sin(9*x)    ||  |    /        3\                              |                            x + 2*log\5*x /    |      /                                              4 /        3\         2          /        3\              2               \                        |1 + -| *atan\-1 + 7*x /          /        3\               |    /        3\                              |              21*x *|1 + -|               9*|1 + -|*atan\-1 + 7*x /*cos(9*x)|
/         /   2\\                |\  \1 + \-1 + 7*x /                              /                                               /      |       /        3\         14*x          294*x *\-1 + 7*x /   54*cos (9*x)*atan\-1 + 7*x /         126*x *cos(9*x)      |    /         /   2\\   \    x/                     4*atan\-1 + 7*x /               \1 + \-1 + 7*x /                              /                    \    x/                 \    x/                         |
\x + 2*log\5*x //               *|--------------------------------------------------------------------------------------------------- + 3*|27*atan\-1 + 7*x / + ---------------- - ------------------- + ---------------------------- - ---------------------------|*log\x + 2*log\5*x // - ------------------------ - -------------------- + --------------------------------------------------------- + ------------------------------------ - ----------------------------------|
                                 |                                              sin(9*x)                                                  |                                    2                     2               2                  /               2\         |                                            2       2 /         /   2\\                                 /   2\                        /               2\                         /         /   2\\             |
                                 |                                                                                                        |                         /        3\    /               2\             sin (9*x)             |    /        3\ |         |                           /         /   2\\       x *\x + 2*log\5*x //                        x + 2*log\5*x /                        |    /        3\ | /         /   2\\       \x + 2*log\5*x //*sin(9*x)    |
                                 |                                                                                                        |                     1 + \-1 + 7*x /    |    /        3\ |                                   \1 + \-1 + 7*x / /*sin(9*x)|                           \x + 2*log\5*x //                                                                                          \1 + \-1 + 7*x / /*\x + 2*log\5*x //                                     |
                                 \                                                                                                        \                                        \1 + \-1 + 7*x / /                                                              /                                                                                                                                                                                                               /
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                                                                                                                                                                                                                                      sin(9*x)                                                                                                                                                                                                                                      
$$\frac{1}{\sin{\left (9 x \right )}} \left(x + 2 \log{\left (5 x^{2} \right )}\right)^{\frac{\operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}}} \left(\frac{21 x^{2} \left(1 + \frac{4}{x}\right)}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \left(\left(7 x^{3} - 1\right)^{2} + 1\right)} - \frac{\left(1 + \frac{4}{x}\right)^{2} \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right)^{2}} + \frac{3}{x + 2 \log{\left (5 x^{2} \right )}} \left(1 + \frac{4}{x}\right) \left(\frac{7 x^{2}}{\left(7 x^{3} - 1\right)^{2} + 1} - \frac{3 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}} \cos{\left (9 x \right )}\right) - \frac{9 \left(1 + \frac{4}{x}\right) \cos{\left (9 x \right )} \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \sin{\left (9 x \right )}} + \frac{1}{\sin{\left (9 x \right )}} \left(\frac{\left(1 + \frac{4}{x}\right) \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{x + 2 \log{\left (5 x^{2} \right )}} + 3 \left(\frac{7 x^{2}}{\left(7 x^{3} - 1\right)^{2} + 1} - \frac{3 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}} \cos{\left (9 x \right )}\right) \log{\left (x + 2 \log{\left (5 x^{2} \right )} \right )}\right)^{2} + 3 \left(- \frac{294 x^{4} \left(7 x^{3} - 1\right)}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right)^{2}} - \frac{126 x^{2} \cos{\left (9 x \right )}}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right) \sin{\left (9 x \right )}} + \frac{14 x}{\left(7 x^{3} - 1\right)^{2} + 1} + 27 \operatorname{atan}{\left (7 x^{3} - 1 \right )} + \frac{54 \cos^{2}{\left (9 x \right )}}{\sin^{2}{\left (9 x \right )}} \operatorname{atan}{\left (7 x^{3} - 1 \right )}\right) \log{\left (x + 2 \log{\left (5 x^{2} \right )} \right )} - \frac{4 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{x^{2} \left(x + 2 \log{\left (5 x^{2} \right )}\right)}\right)$$
Третья производная
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                                 /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                                                                                                                                                                                                                /         2               /        3\         \                                                                            \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \
                                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |                                                                                                                                                                                                        /    4\ |      7*x          3*atan\-1 + 7*x /*cos(9*x)|                                                                            |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
                                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |                                                                                                                                                           2                                          3*|1 + -|*|---------------- - --------------------------|                                                                            |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
                                 |                                                                                                  3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           /                                                                         /    4\     /        3\\ |                                                                                                                                                    /    4\      /        3\                            \    x/ |               2            sin(9*x)         |                  2 /    4\                 /    4\     /        3\         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
                                 |/                                                                         /    4\     /        3\\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |  /         2               /        3\         \                        |1 + -|*atan\-1 + 7*x /| |  /                                              4 /        3\         2          /        3\              2               \                        |1 + -| *atan\-1 + 7*x /          /        3\               |    /        3\                              |              21*x *|1 + -|               9*|1 + -|*atan\-1 + 7*x /*cos(9*x)|             /                                              4 /        3\         2          /        3\              2               \                                                                                                                                                                                                                                                                                                                                                                       |
                                 ||  /         2               /        3\         \                        |1 + -|*atan\-1 + 7*x /|                                                                                                                                                                                                                                                                                                                                              /         2               /        3\         \            2 /         2               /        3\         \                                  |  |      7*x          3*atan\-1 + 7*x /*cos(9*x)|    /         /   2\\   \    x/                | |  |       /        3\         14*x          294*x *\-1 + 7*x /   54*cos (9*x)*atan\-1 + 7*x /         126*x *cos(9*x)      |    /         /   2\\   \    x/                     4*atan\-1 + 7*x /               \1 + \-1 + 7*x /                              /                    \    x/                 \    x/                         |     /    4\ |       /        3\         14*x          294*x *\-1 + 7*x /   54*cos (9*x)*atan\-1 + 7*x /         126*x *cos(9*x)      |                                                                                                                                                                                                                                                                                                                                                                       |
                     /        3\ ||  |      7*x          3*atan\-1 + 7*x /*cos(9*x)|    /         /   2\\   \    x/                |                                                                                                                                                                                                                                                                                                                                              |      7*x          3*atan\-1 + 7*x /*cos(9*x)|     /    4\  |      7*x          3*atan\-1 + 7*x /*cos(9*x)|                                3*|3*|---------------- - --------------------------|*log\x + 2*log\5*x // + -----------------------|*|3*|27*atan\-1 + 7*x / + ---------------- - ------------------- + ---------------------------- - ---------------------------|*log\x + 2*log\5*x // - ------------------------ - -------------------- + --------------------------------------------------------- + ------------------------------------ - ----------------------------------|   6*|1 + -|*|27*atan\-1 + 7*x / + ---------------- - ------------------- + ---------------------------- - ---------------------------|                                                                                                                                                                                                                                                                                                                                                                       |
                 atan\-1 + 7*x / ||3*|---------------- - --------------------------|*log\x + 2*log\5*x // + -----------------------|                                                                                                                                                                                                                                                                                                                                           12*|---------------- - --------------------------|   3*|1 + -| *|---------------- - --------------------------|            3                     |  |               2            sin(9*x)         |                                     /   2\    | |  |                                    2                     2               2                  /               2\         |                                            2       2 /         /   2\\                                 /   2\                        /               2\                         /         /   2\\             |     \    x/ |                                    2                     2               2                  /               2\         |                                                                                2                                                                                                                                    2                                                                                                                                                 |
                 --------------- ||  |               2            sin(9*x)         |                                     /   2\    |                                             /                                                                                                                                                                       2                                                                                            \                           |               2            sin(9*x)         |     \    x/  |               2            sin(9*x)         |     /    4\      /        3\     |  |    /        3\                              |                            x + 2*log\5*x /    | |  |                         /        3\    /               2\             sin (9*x)             |    /        3\ |         |                           /         /   2\\       x *\x + 2*log\5*x //                        x + 2*log\5*x /                        |    /        3\ | /         /   2\\       \x + 2*log\5*x //*sin(9*x)    |             |                         /        3\    /               2\             sin (9*x)             |    /        3\ |         |                             /    4\     /        3\                   2 /    4\                  /    4\     /        3\                    /    4\                          4 /    4\ /        3\           /    4\      /        3\                                                   2      /    4\     /        3\                   2 /    4\                    |
                     sin(9*x)    ||  |    /        3\                              |                            x + 2*log\5*x /    |                                             |                               6                   2              3 /        3\           3          /        3\            /        3\                   6 /        3\                                             2    2                    4 /        3\         |                           |    /        3\                              |              |    /        3\                              |   2*|1 + -| *atan\-1 + 7*x /     \  \1 + \-1 + 7*x /                              /                                               / |  |                     1 + \-1 + 7*x /    |    /        3\ |                                   \1 + \-1 + 7*x / /*sin(9*x)|                           \x + 2*log\5*x //                                                                                          \1 + \-1 + 7*x / /*\x + 2*log\5*x //                                     |             |                     1 + \-1 + 7*x /    |    /        3\ |                                   \1 + \-1 + 7*x / /*sin(9*x)|          /        3\     81*|1 + -|*atan\-1 + 7*x /               42*x *|1 + -|               12*|1 + -|*atan\-1 + 7*x /               42*x*|1 + -|                     882*x *|1 + -|*\-1 + 7*x /        18*|1 + -| *atan\-1 + 7*x /*cos(9*x)           /        3\             162*cos (9*x)*|1 + -|*atan\-1 + 7*x /              378*x *|1 + -|*cos(9*x)           |
/         /   2\\                |\  \1 + \-1 + 7*x /                              /                                               /                    168                      |       14                6174*x              1701*x         1764*x *\-1 + 7*x /   1458*cos (9*x)*atan\-1 + 7*x /   1215*atan\-1 + 7*x /*cos(9*x)   24696*x *\-1 + 7*x /           378*x*cos(9*x)              3402*x *cos (9*x)         7938*x *\-1 + 7*x /*cos(9*x)|    /         /   2\\      \1 + \-1 + 7*x /                              /              \1 + \-1 + 7*x /                              /     \    x/                                                                                                                         \  \                                        \1 + \-1 + 7*x / /                                                              /                                                                                                                                                                                                               /             \                                        \1 + \-1 + 7*x / /                                                              /    8*atan\-1 + 7*x /        \    x/                                     \    x/                  \    x/                                    \    x/                            \    x/                       \    x/                              72*atan\-1 + 7*x /*cos(9*x)                  \    x/                                     \    x/                    |
\x + 2*log\5*x //               *|--------------------------------------------------------------------------------------------------- - ------------------------------------ + 3*|---------------- - ------------------- + ---------------- - ------------------- - ------------------------------ - ----------------------------- + --------------------- - --------------------------- + ---------------------------- + ----------------------------|*log\x + 2*log\5*x // - -------------------------------------------------- - ---------------------------------------------------------- + -------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------ + -------------------- + -------------------------- - ------------------------------------- + -------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------ + ----------------------------- + ------------------------------------- - ---------------------------------------------|
                                 |                                                2                                                     /               2\                       |               2                     2                  2                     2                3                              sin(9*x)                                3    /               2\            /               2\                               2         |                                        2 /         /   2\\                                                       2                                            3                                                                                                                                                                                                                            sin(9*x)                                                                                                                                                                                                                                                                                           /   2\                                                               3 /         /   2\\                 /   2\         /               2\                  2                         2      /               2\                                       2                                          2                  2 /         /   2\\                 /         /   2\\    2             /               2\                           |
                                 |                                             sin (9*x)                                                |    /        3\ | /         /   2\\     |    /        3\    /               2\        /        3\    /               2\              sin (9*x)                                               /               2\     |    /        3\ |            |    /        3\ |    2        /               2\          |                                       x *\x + 2*log\5*x //                                      /         /   2\\                            /         /   2\\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       x + 2*log\5*x /                                                              x *\x + 2*log\5*x //        x + 2*log\5*x /         |    /        3\ | /         /   2\\       2 /         /   2\\       |    /        3\ | /         /   2\\   /               2\                          /         /   2\\                  x *\x + 2*log\5*x //*sin(9*x)        \x + 2*log\5*x //*sin (9*x)        |    /        3\ | /         /   2\\         |
                                 |                                                                                                      \1 + \-1 + 7*x / /*\x + 2*log\5*x //     |1 + \-1 + 7*x /    |    /        3\ |    1 + \-1 + 7*x /    |    /        3\ |                                                                      |    /        3\ |     \1 + \-1 + 7*x / /*sin(9*x)   \1 + \-1 + 7*x / /*sin (9*x)   |    /        3\ |          |                                                                                                 \x + 2*log\5*x //                            \x + 2*log\5*x //                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \1 + \-1 + 7*x / /*\x + 2*log\5*x //      x *\x + 2*log\5*x //       \1 + \-1 + 7*x / /*\x + 2*log\5*x //   |    /        3\ |  /         /   2\\       \x + 2*log\5*x // *sin(9*x)                                                                                \1 + \-1 + 7*x / /*\x + 2*log\5*x //*sin(9*x)|
                                 \                                                                                                                                               \                   \1 + \-1 + 7*x / /                       \1 + \-1 + 7*x / /                                                                      \1 + \-1 + 7*x / /                                                                  \1 + \-1 + 7*x / / *sin(9*x)/                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \1 + \-1 + 7*x / / *\x + 2*log\5*x //                                                                                                                                                               /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            sin(9*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           
$$\frac{1}{\sin{\left (9 x \right )}} \left(x + 2 \log{\left (5 x^{2} \right )}\right)^{\frac{\operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}}} \left(- \frac{882 x^{4} \left(1 + \frac{4}{x}\right) \left(7 x^{3} - 1\right)}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \left(\left(7 x^{3} - 1\right)^{2} + 1\right)^{2}} - \frac{42 x^{2} \left(1 + \frac{4}{x}\right)^{2}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right)^{2} \left(\left(7 x^{3} - 1\right)^{2} + 1\right)} - \frac{378 x^{2} \left(1 + \frac{4}{x}\right) \cos{\left (9 x \right )}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \left(\left(7 x^{3} - 1\right)^{2} + 1\right) \sin{\left (9 x \right )}} + \frac{42 x \left(1 + \frac{4}{x}\right)}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \left(\left(7 x^{3} - 1\right)^{2} + 1\right)} + \frac{2 \left(1 + \frac{4}{x}\right)^{3} \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right)^{3}} - \frac{3 \left(1 + \frac{4}{x}\right)^{2}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right)^{2}} \left(\frac{7 x^{2}}{\left(7 x^{3} - 1\right)^{2} + 1} - \frac{3 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}} \cos{\left (9 x \right )}\right) + \frac{18 \left(1 + \frac{4}{x}\right)^{2} \cos{\left (9 x \right )} \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right)^{2} \sin{\left (9 x \right )}} + \frac{6}{x + 2 \log{\left (5 x^{2} \right )}} \left(1 + \frac{4}{x}\right) \left(- \frac{294 x^{4} \left(7 x^{3} - 1\right)}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right)^{2}} - \frac{126 x^{2} \cos{\left (9 x \right )}}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right) \sin{\left (9 x \right )}} + \frac{14 x}{\left(7 x^{3} - 1\right)^{2} + 1} + 27 \operatorname{atan}{\left (7 x^{3} - 1 \right )} + \frac{54 \cos^{2}{\left (9 x \right )}}{\sin^{2}{\left (9 x \right )}} \operatorname{atan}{\left (7 x^{3} - 1 \right )}\right) + \frac{81 \left(1 + \frac{4}{x}\right) \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{x + 2 \log{\left (5 x^{2} \right )}} + \frac{162 \left(1 + \frac{4}{x}\right) \cos^{2}{\left (9 x \right )} \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \sin^{2}{\left (9 x \right )}} + \frac{1}{\sin^{2}{\left (9 x \right )}} \left(\frac{\left(1 + \frac{4}{x}\right) \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{x + 2 \log{\left (5 x^{2} \right )}} + 3 \left(\frac{7 x^{2}}{\left(7 x^{3} - 1\right)^{2} + 1} - \frac{3 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}} \cos{\left (9 x \right )}\right) \log{\left (x + 2 \log{\left (5 x^{2} \right )} \right )}\right)^{3} + \frac{3}{\sin{\left (9 x \right )}} \left(\frac{\left(1 + \frac{4}{x}\right) \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{x + 2 \log{\left (5 x^{2} \right )}} + 3 \left(\frac{7 x^{2}}{\left(7 x^{3} - 1\right)^{2} + 1} - \frac{3 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}} \cos{\left (9 x \right )}\right) \log{\left (x + 2 \log{\left (5 x^{2} \right )} \right )}\right) \left(\frac{21 x^{2} \left(1 + \frac{4}{x}\right)}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \left(\left(7 x^{3} - 1\right)^{2} + 1\right)} - \frac{\left(1 + \frac{4}{x}\right)^{2} \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right)^{2}} + \frac{3}{x + 2 \log{\left (5 x^{2} \right )}} \left(1 + \frac{4}{x}\right) \left(\frac{7 x^{2}}{\left(7 x^{3} - 1\right)^{2} + 1} - \frac{3 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}} \cos{\left (9 x \right )}\right) - \frac{9 \left(1 + \frac{4}{x}\right) \cos{\left (9 x \right )} \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \sin{\left (9 x \right )}} + 3 \left(- \frac{294 x^{4} \left(7 x^{3} - 1\right)}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right)^{2}} - \frac{126 x^{2} \cos{\left (9 x \right )}}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right) \sin{\left (9 x \right )}} + \frac{14 x}{\left(7 x^{3} - 1\right)^{2} + 1} + 27 \operatorname{atan}{\left (7 x^{3} - 1 \right )} + \frac{54 \cos^{2}{\left (9 x \right )}}{\sin^{2}{\left (9 x \right )}} \operatorname{atan}{\left (7 x^{3} - 1 \right )}\right) \log{\left (x + 2 \log{\left (5 x^{2} \right )} \right )} - \frac{4 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{x^{2} \left(x + 2 \log{\left (5 x^{2} \right )}\right)}\right) + 3 \left(\frac{24696 x^{6} \left(7 x^{3} - 1\right)^{2}}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right)^{3}} - \frac{6174 x^{6}}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right)^{2}} + \frac{7938 x^{4} \left(7 x^{3} - 1\right) \cos{\left (9 x \right )}}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right)^{2} \sin{\left (9 x \right )}} - \frac{1764 x^{3} \left(7 x^{3} - 1\right)}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right)^{2}} + \frac{1701 x^{2}}{\left(7 x^{3} - 1\right)^{2} + 1} + \frac{3402 x^{2} \cos^{2}{\left (9 x \right )}}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right) \sin^{2}{\left (9 x \right )}} - \frac{378 x \cos{\left (9 x \right )}}{\left(\left(7 x^{3} - 1\right)^{2} + 1\right) \sin{\left (9 x \right )}} - \frac{1215 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}} \cos{\left (9 x \right )} - \frac{1458 \cos^{3}{\left (9 x \right )}}{\sin^{3}{\left (9 x \right )}} \operatorname{atan}{\left (7 x^{3} - 1 \right )} + \frac{14}{\left(7 x^{3} - 1\right)^{2} + 1}\right) \log{\left (x + 2 \log{\left (5 x^{2} \right )} \right )} - \frac{168}{\left(x + 2 \log{\left (5 x^{2} \right )}\right) \left(\left(7 x^{3} - 1\right)^{2} + 1\right)} + \frac{12 \left(1 + \frac{4}{x}\right) \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{x^{2} \left(x + 2 \log{\left (5 x^{2} \right )}\right)^{2}} - \frac{1}{x^{2} \left(x + 2 \log{\left (5 x^{2} \right )}\right)} \left(\frac{84 x^{2}}{\left(7 x^{3} - 1\right)^{2} + 1} - \frac{36 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{\sin{\left (9 x \right )}} \cos{\left (9 x \right )}\right) + \frac{72 \cos{\left (9 x \right )} \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{x^{2} \left(x + 2 \log{\left (5 x^{2} \right )}\right) \sin{\left (9 x \right )}} + \frac{8 \operatorname{atan}{\left (7 x^{3} - 1 \right )}}{x^{3} \left(x + 2 \log{\left (5 x^{2} \right )}\right)}\right)$$