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- Derivative of:
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Derivative of 9/x
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Derivative of x^-5
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Derivative of x^2*e^x
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Derivative of x^2*cos(x)
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Identical expressions
- atan(sin(log(x^ ten +e^(four *x))^ nine)^ eight)^ seven
- arc tangent of gent of ( sinus of ( logarithm of (x to the power of 10 plus e to the power of (4 multiply by x)) to the power of 9) to the power of 8) to the power of 7
- arc tangent of gent of ( sinus of ( logarithm of (x to the power of ten plus e to the power of (four multiply by x)) to the power of nine) to the power of eight) to the power of seven
- atan(sin(log(x10+e(4*x))9)8)7
- atansinlogx10+e4*x987
- atan(sin(log(x^10+e^(4*x))⁹)⁸)⁷
- atan(sin(log(x^10+e^(4x))^9)^8)^7
- atan(sin(log(x10+e(4x))9)8)7
- atansinlogx10+e4x987
- atansinlogx^10+e^4x^9^8^7
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Similar expressions
- atan(sin(log(x^10-e^(4*x))^9)^8)^7
- arctan(sin(log(x^10+e^(4*x))^9)^8)^7
Derivative of atan(sin(log(x^10+e^(4*x))^9)^8)^7
The solution
You have entered
[src]
7/ 8/ 9/ 10 4*x\\\ atan \sin \log \x + e ///
$$\operatorname{atan}^{7}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}$$
d / 7/ 8/ 9/ 10 4*x\\\\ --\atan \sin \log \x + e //// dx
$$\frac{d}{d x} \operatorname{atan}^{7}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}$$
The first derivative
[src]
6/ 8/ 9/ 10 4*x\\\ 8/ 10 4*x\ 7/ 9/ 10 4*x\\ / 4*x 9\ / 9/ 10 4*x\\
504*atan \sin \log \x + e ///*log \x + e /*sin \log \x + e //*\4*e + 10*x /*cos\log \x + e //
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/ 16/ 9/ 10 4*x\\\ / 10 4*x\
\1 + sin \log \x + e ///*\x + e /
$$\frac{504 \cdot \left(10 x^{9} + 4 e^{4 x}\right) \log{\left(x^{10} + e^{4 x} \right)}^{8} \sin^{7}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{6}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right) \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)}$$
The second derivative
[src]
/ 2 2 2 2 2 2 \
| / 4*x 9\ 9/ 10 4*x\ 2/ 9/ 10 4*x\\ / 8/ 9/ 10 4*x\\\ / 4*x 9\ / 8/ 9/ 10 4*x\\\ / 9/ 10 4*x\\ / 9/ 10 4*x\\ / 4*x 9\ 2/ 9/ 10 4*x\\ 9/ 10 4*x\ / 8/ 9/ 10 4*x\\\ / 4*x 9\ / 8/ 9/ 10 4*x\\\ / 9/ 10 4*x\\ / 10 4*x\ / 9/ 10 4*x\\ / 4*x 9\ 2/ 9/ 10 4*x\\ 9/ 10 4*x\ 8/ 9/ 10 4*x\\ / 4*x 9\ 2/ 9/ 10 4*x\\ 9/ 10 4*x\ 16/ 9/ 10 4*x\\ / 8/ 9/ 10 4*x\\\|
5/ 8/ 9/ 10 4*x\\\ 7/ 10 4*x\ 6/ 9/ 10 4*x\\ |/ 4*x 8\ / 8/ 9/ 10 4*x\\\ / 9/ 10 4*x\\ / 10 4*x\ / 9/ 10 4*x\\ 18*\2*e + 5*x / *log \x + e /*sin \log \x + e //*atan\sin \log \x + e /// 16*\2*e + 5*x / *atan\sin \log \x + e ///*cos\log \x + e //*sin\log \x + e // 126*\2*e + 5*x / *cos \log \x + e //*log \x + e /*atan\sin \log \x + e /// 2*\2*e + 5*x / *atan\sin \log \x + e ///*cos\log \x + e //*log\x + e /*sin\log \x + e // 864*\2*e + 5*x / *cos \log \x + e //*log \x + e /*sin \log \x + e // 288*\2*e + 5*x / *cos \log \x + e //*log \x + e /*sin \log \x + e //*atan\sin \log \x + e ///|
1008*atan \sin \log \x + e ///*log \x + e /*sin \log \x + e //*|\8*e + 45*x /*atan\sin \log \x + e ///*cos\log \x + e //*log\x + e /*sin\log \x + e // - ---------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------|
| 10 4*x 10 4*x 10 4*x 10 4*x / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ |
\ x + e x + e x + e x + e \1 + sin \log \x + e ///*\x + e / \1 + sin \log \x + e ///*\x + e / /
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/ 16/ 9/ 10 4*x\\\ / 10 4*x\
\1 + sin \log \x + e ///*\x + e /
$$\frac{1008 \left(- \frac{288 \left(5 x^{9} + 2 e^{4 x}\right)^{2} \log{\left(x^{10} + e^{4 x} \right)}^{9} \sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right) \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} + \frac{864 \left(5 x^{9} + 2 e^{4 x}\right)^{2} \log{\left(x^{10} + e^{4 x} \right)}^{9} \sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)}}{\left(x^{10} + e^{4 x}\right) \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} - \frac{18 \left(5 x^{9} + 2 e^{4 x}\right)^{2} \log{\left(x^{10} + e^{4 x} \right)}^{9} \sin^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{x^{10} + e^{4 x}} + \frac{126 \left(5 x^{9} + 2 e^{4 x}\right)^{2} \log{\left(x^{10} + e^{4 x} \right)}^{9} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{x^{10} + e^{4 x}} + \left(45 x^{8} + 8 e^{4 x}\right) \log{\left(x^{10} + e^{4 x} \right)} \sin{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)} - \frac{2 \left(5 x^{9} + 2 e^{4 x}\right)^{2} \log{\left(x^{10} + e^{4 x} \right)} \sin{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{x^{10} + e^{4 x}} + \frac{16 \left(5 x^{9} + 2 e^{4 x}\right)^{2} \sin{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{x^{10} + e^{4 x}}\right) \log{\left(x^{10} + e^{4 x} \right)}^{7} \sin^{6}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{5}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right) \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)}$$
The third derivative
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/ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 \
| / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 9/ 10 4*x\ 3/ 9/ 10 4*x\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 10/ 10 4*x\ 3/ 9/ 10 4*x\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 2/ 9/ 10 4*x\\ / 9/ 10 4*x\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 3/ 9/ 10 4*x\\ 18/ 10 4*x\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 18/ 10 4*x\ 2/ 9/ 10 4*x\\ / 9/ 10 4*x\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 2/ 9/ 10 4*x\\ 10/ 10 4*x\ / 9/ 10 4*x\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 2/ 9/ 10 4*x\\ / 9/ 10 4*x\\ / 10 4*x\ 2/ 8/ 9/ 10 4*x\\\ 10/ 10 4*x\ 3/ 9/ 10 4*x\\ / 4*x 9\ / 4*x 8\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 2/ 10 4*x\ 2/ 9/ 10 4*x\\ / 9/ 10 4*x\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 2/ 9/ 10 4*x\\ 9/ 10 4*x\ / 9/ 10 4*x\\ / 4*x 9\ 3/ 9/ 10 4*x\\ 18/ 10 4*x\ 16/ 9/ 10 4*x\\ / 4*x 9\ 3/ 9/ 10 4*x\\ 18/ 10 4*x\ 24/ 9/ 10 4*x\\ / 8/ 9/ 10 4*x\\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 3/ 9/ 10 4*x\\ 18/ 10 4*x\ 16/ 9/ 10 4*x\\ / 4*x 9\ 18/ 10 4*x\ 10/ 9/ 10 4*x\\ / 8/ 9/ 10 4*x\\\ / 9/ 10 4*x\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 2/ 9/ 10 4*x\\ 9/ 10 4*x\ 17/ 9/ 10 4*x\\ / 4*x 9\ 2/ 9/ 10 4*x\\ 10/ 10 4*x\ 9/ 9/ 10 4*x\\ / 8/ 9/ 10 4*x\\\ 2/ 8/ 9/ 10 4*x\\\ 2/ 10 4*x\ 2/ 9/ 10 4*x\\ / 4*x 9\ / 4*x 8\ / 9/ 10 4*x\\ 2/ 8/ 9/ 10 4*x\\\ 2/ 9/ 10 4*x\\ / 4*x 9\ / 4*x 8\ / 9/ 10 4*x\\ / 10 4*x\ 2/ 8/ 9/ 10 4*x\\\ 2/ 9/ 10 4*x\\ 10/ 10 4*x\ / 4*x 9\ / 4*x 8\ / 9/ 10 4*x\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 2/ 9/ 10 4*x\\ 10/ 10 4*x\ 17/ 9/ 10 4*x\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 18/ 10 4*x\ 18/ 9/ 10 4*x\\ / 9/ 10 4*x\\ / 4*x 9\ 2/ 9/ 10 4*x\\ 9/ 10 4*x\ 9/ 9/ 10 4*x\\ / 8/ 9/ 10 4*x\\\ / 4*x 9\ 2/ 8/ 9/ 10 4*x\\\ 3/ 9/ 10 4*x\\ 18/ 10 4*x\ 32/ 9/ 10 4*x\\ / 4*x 9\ 3/ 9/ 10 4*x\\ 18/ 10 4*x\ 8/ 9/ 10 4*x\\ / 8/ 9/ 10 4*x\\\ 2/ 8/ 9/ 10 4*x\\\ 2/ 9/ 10 4*x\\ 10/ 10 4*x\ 17/ 9/ 10 4*x\\ / 4*x 9\ / 4*x 8\ 2/ 9/ 10 4*x\\ 10/ 10 4*x\ 9/ 9/ 10 4*x\\ / 4*x 9\ / 4*x 8\ / 8/ 9/ 10 4*x\\\|
4/ 8/ 9/ 10 4*x\\\ 6/ 10 4*x\ 5/ 9/ 10 4*x\\ | 432*\2*e + 5*x / *atan \sin \log \x + e ///*log \x + e /*sin \log \x + e // 2/ 8/ 9/ 10 4*x\\\ 2/ 10 4*x\ 2/ 9/ 10 4*x\\ / 4*x 7\ / 9/ 10 4*x\\ 54*\2*e + 5*x / *atan \sin \log \x + e ///*log \x + e /*sin \log \x + e // 112*\2*e + 5*x / *atan \sin \log \x + e ///*sin \log \x + e //*cos\log \x + e // 6804*\2*e + 5*x / *atan \sin \log \x + e ///*cos \log \x + e //*log \x + e / 3564*\2*e + 5*x / *atan \sin \log \x + e ///*log \x + e /*sin \log \x + e //*cos\log \x + e // 378*\2*e + 5*x / *atan \sin \log \x + e ///*cos \log \x + e //*log \x + e /*sin\log \x + e // 48*\2*e + 5*x / *atan \sin \log \x + e ///*sin \log \x + e //*cos\log \x + e //*log\x + e / 27*atan \sin \log \x + e ///*log \x + e /*sin \log \x + e //*\2*e + 5*x /*\8*e + 45*x / 4*\2*e + 5*x / *atan \sin \log \x + e ///*log \x + e /*sin \log \x + e //*cos\log \x + e // 3024*\2*e + 5*x / *atan \sin \log \x + e ///*cos \log \x + e //*log \x + e /*sin\log \x + e // 311040*\2*e + 5*x / *cos \log \x + e //*log \x + e /*sin \log \x + e // 373248*\2*e + 5*x / *cos \log \x + e //*log \x + e /*sin \log \x + e //*atan\sin \log \x + e /// 75168*\2*e + 5*x / *atan \sin \log \x + e ///*cos \log \x + e //*log \x + e /*sin \log \x + e // 23328*\2*e + 5*x / *log \x + e /*sin \log \x + e //*atan\sin \log \x + e ///*cos\log \x + e // 6912*\2*e + 5*x / *atan \sin \log \x + e ///*cos \log \x + e //*log \x + e /*sin \log \x + e // 2592*\2*e + 5*x / *cos \log \x + e //*log \x + e /*sin \log \x + e //*atan\sin \log \x + e /// 3*atan \sin \log \x + e ///*log \x + e /*sin \log \x + e //*\2*e + 5*x /*\8*e + 45*x /*cos\log \x + e // 24*atan \sin \log \x + e ///*sin \log \x + e //*\2*e + 5*x /*\8*e + 45*x /*cos\log \x + e //*log\x + e / 189*atan \sin \log \x + e ///*cos \log \x + e //*log \x + e /*\2*e + 5*x /*\8*e + 45*x /*sin\log \x + e // 864*\2*e + 5*x / *atan \sin \log \x + e ///*cos \log \x + e //*log \x + e /*sin \log \x + e // 7776*\2*e + 5*x / *atan \sin \log \x + e ///*log \x + e /*sin \log \x + e //*cos\log \x + e // 20736*\2*e + 5*x / *cos \log \x + e //*log \x + e /*sin \log \x + e //*atan\sin \log \x + e /// 82944*\2*e + 5*x / *atan \sin \log \x + e ///*cos \log \x + e //*log \x + e /*sin \log \x + e // 163296*\2*e + 5*x / *cos \log \x + e //*log \x + e /*sin \log \x + e //*atan\sin \log \x + e /// 432*atan \sin \log \x + e ///*cos \log \x + e //*log \x + e /*sin \log \x + e //*\2*e + 5*x /*\8*e + 45*x / 1296*cos \log \x + e //*log \x + e /*sin \log \x + e //*\2*e + 5*x /*\8*e + 45*x /*atan\sin \log \x + e ///|
2016*atan \sin \log \x + e ///*log \x + e /*sin \log \x + e //*|- ------------------------------------------------------------------------------------------ + 4*atan \sin \log \x + e ///*log \x + e /*sin \log \x + e //*\4*e + 45*x /*cos\log \x + e // + ------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------|
| 2 2 2 2 2 2 2 10 4*x 2 2 2 2 2 2 2 2 2 2 10 4*x 10 4*x 10 4*x 2 2 2 2 2 2 / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ |
| / 10 4*x\ / 10 4*x\ / 10 4*x\ / 10 4*x\ / 10 4*x\ / 10 4*x\ / 10 4*x\ x + e / 10 4*x\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ x + e x + e x + e / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ / 16/ 9/ 10 4*x\\\ / 10 4*x\ \1 + sin \log \x + e ///*\x + e / \1 + sin \log \x + e ///*\x + e / |
\ \x + e / \x + e / \x + e / \x + e / \x + e / \x + e / \x + e / \x + e / \x + e / \1 + sin \log \x + e /// *\x + e / \1 + sin \log \x + e /// *\x + e / \1 + sin \log \x + e ///*\x + e / \1 + sin \log \x + e ///*\x + e / \1 + sin \log \x + e ///*\x + e / \1 + sin \log \x + e ///*\x + e / \1 + sin \log \x + e ///*\x + e / \1 + sin \log \x + e ///*\x + e / \1 + sin \log \x + e ///*\x + e / \1 + sin \log \x + e /// *\x + e / \1 + sin \log \x + e ///*\x + e / /
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/ 16/ 9/ 10 4*x\\\ / 10 4*x\
\1 + sin \log \x + e ///*\x + e /
$$\frac{2016 \cdot \left(\frac{82944 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{18} \sin^{32}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{3}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)^{2}} - \frac{373248 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{18} \sin^{24}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{3}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)^{2}} + \frac{7776 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{18} \sin^{18}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} - \frac{75168 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{18} \sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{3}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} + \frac{311040 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{18} \sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{3}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)^{2}} - \frac{432 \cdot \left(45 x^{8} + 8 e^{4 x}\right) \left(5 x^{9} + 2 e^{4 x}\right) \log{\left(x^{10} + e^{4 x} \right)}^{10} \sin^{17}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right) \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} + \frac{864 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{10} \sin^{17}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} - \frac{23328 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{18} \sin^{10}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} + \frac{163296 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{18} \sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{3}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} - \frac{6912 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{9} \sin^{17}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} - \frac{3564 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{18} \sin^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2}} + \frac{6804 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{18} \cos^{3}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2}} + \frac{1296 \cdot \left(45 x^{8} + 8 e^{4 x}\right) \left(5 x^{9} + 2 e^{4 x}\right) \log{\left(x^{10} + e^{4 x} \right)}^{10} \sin^{9}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right) \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} - \frac{2592 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{10} \sin^{9}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} + \frac{20736 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{9} \sin^{9}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2} \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)} - \frac{27 \cdot \left(45 x^{8} + 8 e^{4 x}\right) \left(5 x^{9} + 2 e^{4 x}\right) \log{\left(x^{10} + e^{4 x} \right)}^{10} \sin^{3}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{x^{10} + e^{4 x}} + \frac{189 \cdot \left(45 x^{8} + 8 e^{4 x}\right) \left(5 x^{9} + 2 e^{4 x}\right) \log{\left(x^{10} + e^{4 x} \right)}^{10} \sin{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{x^{10} + e^{4 x}} + \frac{54 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{10} \sin^{3}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2}} - \frac{378 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{10} \sin{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2}} - \frac{432 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{9} \sin^{3}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2}} + \frac{3024 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{9} \sin{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2}} + 4 \cdot \left(45 x^{7} + 4 e^{4 x}\right) \log{\left(x^{10} + e^{4 x} \right)}^{2} \sin^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)} - \frac{3 \cdot \left(45 x^{8} + 8 e^{4 x}\right) \left(5 x^{9} + 2 e^{4 x}\right) \log{\left(x^{10} + e^{4 x} \right)}^{2} \sin^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{x^{10} + e^{4 x}} + \frac{4 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)}^{2} \sin^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2}} + \frac{24 \cdot \left(45 x^{8} + 8 e^{4 x}\right) \left(5 x^{9} + 2 e^{4 x}\right) \log{\left(x^{10} + e^{4 x} \right)} \sin^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{x^{10} + e^{4 x}} - \frac{48 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \log{\left(x^{10} + e^{4 x} \right)} \sin^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2}} + \frac{112 \left(5 x^{9} + 2 e^{4 x}\right)^{3} \sin^{2}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \cos{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{2}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right)^{2}}\right) \log{\left(x^{10} + e^{4 x} \right)}^{6} \sin^{5}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \operatorname{atan}^{4}{\left(\sin^{8}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} \right)}}{\left(x^{10} + e^{4 x}\right) \left(\sin^{16}{\left(\log{\left(x^{10} + e^{4 x} \right)}^{9} \right)} + 1\right)}$$
The graph