\(\int \frac {3 x+e^{e^5+x^2} (36-24 x^2)+e^{x^2} (36 x-24 x^3)+(e^{e^5+x^2} (-9+6 x^2)+e^{x^2} (-9 x+6 x^3)) \log (e^{e^5}+x)+(36 e^{e^5}+36 x+(-9 e^{e^5}-9 x) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))+(12 e^{e^5+x^2}+12 e^{x^2} x+(-3 e^{e^5+x^2}-3 e^{x^2} x) \log (e^{e^5}+x)+(12 e^{e^5}+12 x+(-3 e^{e^5}-3 x) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))) \log (\frac {x}{e^{x^2}+\log (-4+\log (e^{e^5}+x))})}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+(4 e^{e^5+x^2} x^2+4 e^{x^2} x^3) \log (e^{e^5}+x)+(-16 e^{e^5} x^2-16 x^3+(4 e^{e^5} x^2+4 x^3) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))+(-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+(4 e^{e^5+x^2} x^2+4 e^{x^2} x^3) \log (e^{e^5}+x)+(-16 e^{e^5} x^2-16 x^3+(4 e^{e^5} x^2+4 x^3) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))) \log (\frac {x}{e^{x^2}+\log (-4+\log (e^{e^5}+x))})+(-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+(e^{e^5+x^2} x^2+e^{x^2} x^3) \log (e^{e^5}+x)+(-4 e^{e^5} x^2-4 x^3+(e^{e^5} x^2+x^3) \log (e^{e^5}+x)) \log (-4+\log (e^{e^5}+x))) \log ^2(\frac {x}{e^{x^2}+\log (-4+\log (e^{e^5}+x))})} \, dx\) [269]

Optimal result

Integrand size = 618, antiderivative size = 31 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )} \] Output:

3/(2+ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2))))/x
 

Mathematica [A] (verified)

Time = 0.32 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \left (2+\log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )\right )} \] Input:

Integrate[(3*x + E^(E^5 + x^2)*(36 - 24*x^2) + E^x^2*(36*x - 24*x^3) + (E^ 
(E^5 + x^2)*(-9 + 6*x^2) + E^x^2*(-9*x + 6*x^3))*Log[E^E^5 + x] + (36*E^E^ 
5 + 36*x + (-9*E^E^5 - 9*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (12 
*E^(E^5 + x^2) + 12*E^x^2*x + (-3*E^(E^5 + x^2) - 3*E^x^2*x)*Log[E^E^5 + x 
] + (12*E^E^5 + 12*x + (-3*E^E^5 - 3*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 
 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])])/(-16*E^(E^5 + x^2)*x^2 
- 16*E^x^2*x^3 + (4*E^(E^5 + x^2)*x^2 + 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16 
*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4*x^3)*Log[E^E^5 + x])*Log[-4 + Log[E 
^E^5 + x]] + (-16*E^(E^5 + x^2)*x^2 - 16*E^x^2*x^3 + (4*E^(E^5 + x^2)*x^2 
+ 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4 
*x^3)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Lo 
g[E^E^5 + x]])] + (-4*E^(E^5 + x^2)*x^2 - 4*E^x^2*x^3 + (E^(E^5 + x^2)*x^2 
 + E^x^2*x^3)*Log[E^E^5 + x] + (-4*E^E^5*x^2 - 4*x^3 + (E^E^5*x^2 + x^3)*L 
og[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 
 + x]])]^2),x]
 

Output:

3/(x*(2 + Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]))
 

Rubi [A] (verified)

Time = 4.23 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {7239, 27, 25, 7238}

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int \frac {e^{x^2+e^5} \left (36-24 x^2\right )+\left (12 e^{x^2} x+12 e^{x^2+e^5}+\left (-3 e^{x^2} x-3 e^{x^2+e^5}\right ) \log \left (x+e^{e^5}\right )+\left (12 x+\left (-3 x-3 e^{e^5}\right ) \log \left (x+e^{e^5}\right )+12 e^{e^5}\right ) \log \left (\log \left (x+e^{e^5}\right )-4\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{x^2+e^5} \left (6 x^2-9\right )+e^{x^2} \left (6 x^3-9 x\right )\right ) \log \left (x+e^{e^5}\right )+3 x+\left (36 x+\left (-9 x-9 e^{e^5}\right ) \log \left (x+e^{e^5}\right )+36 e^{e^5}\right ) \log \left (\log \left (x+e^{e^5}\right )-4\right )}{-16 e^{x^2+e^5} x^2-16 e^{x^2} x^3+\left (-4 e^{x^2+e^5} x^2-4 e^{x^2} x^3+\left (e^{x^2+e^5} x^2+e^{x^2} x^3\right ) \log \left (x+e^{e^5}\right )+\left (-4 x^3-4 e^{e^5} x^2+\left (x^3+e^{e^5} x^2\right ) \log \left (x+e^{e^5}\right )\right ) \log \left (\log \left (x+e^{e^5}\right )-4\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )+\left (4 e^{x^2+e^5} x^2+4 e^{x^2} x^3\right ) \log \left (x+e^{e^5}\right )+\left (-16 x^3-16 e^{e^5} x^2+\left (4 x^3+4 e^{e^5} x^2\right ) \log \left (x+e^{e^5}\right )\right ) \log \left (\log \left (x+e^{e^5}\right )-4\right )+\left (-16 e^{x^2+e^5} x^2-16 e^{x^2} x^3+\left (4 e^{x^2+e^5} x^2+4 e^{x^2} x^3\right ) \log \left (x+e^{e^5}\right )+\left (-16 x^3-16 e^{e^5} x^2+\left (4 x^3+4 e^{e^5} x^2\right ) \log \left (x+e^{e^5}\right )\right ) \log \left (\log \left (x+e^{e^5}\right )-4\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {3 \left (8 e^{x^2+e^5} x^2-12 e^{x^2} x-12 e^{x^2+e^5}-4 e^{x^2} x \log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )-4 e^{x^2+e^5} \log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )-4 \left (x+e^{e^5}\right ) \log \left (\log \left (x+e^{e^5}\right )-4\right ) \left (\log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )+3\right )-\left (x+e^{e^5}\right ) \log \left (x+e^{e^5}\right ) \left (e^{x^2} \left (2 x^2-\log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )-3\right )-\log \left (\log \left (x+e^{e^5}\right )-4\right ) \left (\log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )+3\right )\right )+8 e^{x^2} x^3-x\right )}{x^2 \left (x+e^{e^5}\right ) \left (4-\log \left (x+e^{e^5}\right )\right ) \left (e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )\right ) \left (\log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )+2\right )^2}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 3 \int -\frac {-8 e^{x^2} x^3-8 e^{x^2+e^5} x^2+12 e^{x^2} x+4 e^{x^2} \log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right ) x+x+12 e^{x^2+e^5}+4 e^{x^2+e^5} \log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+4 \left (x+e^{e^5}\right ) \log \left (\log \left (x+e^{e^5}\right )-4\right ) \left (\log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+3\right )-\left (x+e^{e^5}\right ) \log \left (x+e^{e^5}\right ) \left (\log \left (\log \left (x+e^{e^5}\right )-4\right ) \left (\log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+3\right )+e^{x^2} \left (-2 x^2+\log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+3\right )\right )}{x^2 \left (x+e^{e^5}\right ) \left (4-\log \left (x+e^{e^5}\right )\right ) \left (\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}\right ) \left (\log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+2\right )^2}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -3 \int \frac {-8 e^{x^2} x^3-8 e^{x^2+e^5} x^2+12 e^{x^2} x+4 e^{x^2} \log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right ) x+x+12 e^{x^2+e^5}+4 e^{x^2+e^5} \log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+4 \left (x+e^{e^5}\right ) \log \left (\log \left (x+e^{e^5}\right )-4\right ) \left (\log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+3\right )-\left (x+e^{e^5}\right ) \log \left (x+e^{e^5}\right ) \left (\log \left (\log \left (x+e^{e^5}\right )-4\right ) \left (\log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+3\right )+e^{x^2} \left (-2 x^2+\log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+3\right )\right )}{x^2 \left (x+e^{e^5}\right ) \left (4-\log \left (x+e^{e^5}\right )\right ) \left (\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}\right ) \left (\log \left (\frac {x}{\log \left (\log \left (x+e^{e^5}\right )-4\right )+e^{x^2}}\right )+2\right )^2}dx\)

\(\Big \downarrow \) 7238

\(\displaystyle \frac {3}{x \left (\log \left (\frac {x}{e^{x^2}+\log \left (\log \left (x+e^{e^5}\right )-4\right )}\right )+2\right )}\)

Input:

Int[(3*x + E^(E^5 + x^2)*(36 - 24*x^2) + E^x^2*(36*x - 24*x^3) + (E^(E^5 + 
 x^2)*(-9 + 6*x^2) + E^x^2*(-9*x + 6*x^3))*Log[E^E^5 + x] + (36*E^E^5 + 36 
*x + (-9*E^E^5 - 9*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] + (12*E^(E^ 
5 + x^2) + 12*E^x^2*x + (-3*E^(E^5 + x^2) - 3*E^x^2*x)*Log[E^E^5 + x] + (1 
2*E^E^5 + 12*x + (-3*E^E^5 - 3*x)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]] 
)*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])])/(-16*E^(E^5 + x^2)*x^2 - 16*E 
^x^2*x^3 + (4*E^(E^5 + x^2)*x^2 + 4*E^x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5 
*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4*x^3)*Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + 
 x]] + (-16*E^(E^5 + x^2)*x^2 - 16*E^x^2*x^3 + (4*E^(E^5 + x^2)*x^2 + 4*E^ 
x^2*x^3)*Log[E^E^5 + x] + (-16*E^E^5*x^2 - 16*x^3 + (4*E^E^5*x^2 + 4*x^3)* 
Log[E^E^5 + x])*Log[-4 + Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^ 
5 + x]])] + (-4*E^(E^5 + x^2)*x^2 - 4*E^x^2*x^3 + (E^(E^5 + x^2)*x^2 + E^x 
^2*x^3)*Log[E^E^5 + x] + (-4*E^E^5*x^2 - 4*x^3 + (E^E^5*x^2 + x^3)*Log[E^E 
^5 + x])*Log[-4 + Log[E^E^5 + x]])*Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]] 
)]^2),x]
 

Output:

3/(x*(2 + Log[x/(E^x^2 + Log[-4 + Log[E^E^5 + x]])]))
 

Defintions of rubi rules used

rule 25

Int[-(Fx_), x_Symbol] :> Simp[Identity[-1]   Int[Fx, x], x]
 

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 7238

Int[(u_)*(y_)^(m_.)*(z_)^(n_.), x_Symbol] :> With[{q = DerivativeDivides[y* 
z, u*z^(n - m), x]}, Simp[q*y^(m + 1)*(z^(m + 1)/(m + 1)), x] /;  !FalseQ[q 
]] /; FreeQ[{m, n}, x] && NeQ[m, -1]
 

rule 7239

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl 
erIntegrandQ[v, u, x]]
 

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.11 (sec) , antiderivative size = 185, normalized size of antiderivative = 5.97

\[\frac {6 i}{x \left (\pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right ) \operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )-\pi \,\operatorname {csgn}\left (i x \right ) {\operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )}^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right ) {\operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )}^{2}+\pi {\operatorname {csgn}\left (\frac {i x}{\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}}\right )}^{3}+2 i \ln \left (x \right )-2 i \ln \left (\ln \left (\ln \left ({\mathrm e}^{{\mathrm e}^{5}}+x \right )-4\right )+{\mathrm e}^{x^{2}}\right )+4 i\right )}\]

Input:

int(((((-3*exp(exp(5))-3*x)*ln(exp(exp(5))+x)+12*exp(exp(5))+12*x)*ln(ln(e 
xp(exp(5))+x)-4)+(-3*exp(x^2)*exp(exp(5))-3*exp(x^2)*x)*ln(exp(exp(5))+x)+ 
12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x 
^2)))+((-9*exp(exp(5))-9*x)*ln(exp(exp(5))+x)+36*exp(exp(5))+36*x)*ln(ln(e 
xp(exp(5))+x)-4)+((6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9*x)*exp(x^2))*ln( 
exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24*x^3+36*x)*exp(x^2)+3 
*x)/((((x^2*exp(exp(5))+x^3)*ln(exp(exp(5))+x)-4*x^2*exp(exp(5))-4*x^3)*ln 
(ln(exp(exp(5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*exp(x^2))*ln(exp(exp(5 
))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2))*ln(x/(ln(ln(exp(exp(5))+x 
)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*ln(exp(exp(5))+x)-16*x^2*exp 
(exp(5))-16*x^3)*ln(ln(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3 
*exp(x^2))*ln(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2))* 
ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2*exp(exp(5))+4*x^3)*ln(exp 
(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*ln(ln(exp(exp(5))+x)-4)+(4*x^2*exp( 
x^2)*exp(exp(5))+4*x^3*exp(x^2))*ln(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp 
(5))-16*x^3*exp(x^2)),x)
 

Output:

6*I/x/(Pi*csgn(I*x)*csgn(I/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))*csgn(I*x/(l 
n(ln(exp(exp(5))+x)-4)+exp(x^2)))-Pi*csgn(I*x)*csgn(I*x/(ln(ln(exp(exp(5)) 
+x)-4)+exp(x^2)))^2-Pi*csgn(I/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))*csgn(I*x 
/(ln(ln(exp(exp(5))+x)-4)+exp(x^2)))^2+Pi*csgn(I*x/(ln(ln(exp(exp(5))+x)-4 
)+exp(x^2)))^3+2*I*ln(x)-2*I*ln(ln(ln(exp(exp(5))+x)-4)+exp(x^2))+4*I)
 

Fricas [A] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.26 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \log \left (\frac {x e^{\left (e^{5}\right )}}{e^{\left (e^{5}\right )} \log \left (\log \left (x + e^{\left (e^{5}\right )}\right ) - 4\right ) + e^{\left (x^{2} + e^{5}\right )}}\right ) + 2 \, x} \] Input:

integrate(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)* 
log(log(exp(exp(5))+x)-4)+(-3*exp(x^2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(e 
xp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(5) 
)+x)-4)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5)) 
+36*x)*log(log(exp(exp(5))+x)-4)+((6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9* 
x)*exp(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24*x^3 
+36*x)*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp 
(exp(5))-4*x^3)*log(log(exp(exp(5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*ex 
p(x^2))*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2))*log( 
x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log( 
exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2 
*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp(exp(5))+x)-16*x^2*exp(x^2)*e 
xp(exp(5))-16*x^3*exp(x^2))*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+(( 
4*x^2*exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log 
(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp 
(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2)),x, algorithm="fri 
cas")
 

Output:

3/(x*log(x*e^(e^5)/(e^(e^5)*log(log(x + e^(e^5)) - 4) + e^(x^2 + e^5))) + 
2*x)
 

Sympy [F(-1)]

Timed out. \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\text {Timed out} \] Input:

integrate(((((-3*exp(exp(5))-3*x)*ln(exp(exp(5))+x)+12*exp(exp(5))+12*x)*l 
n(ln(exp(exp(5))+x)-4)+(-3*exp(x**2)*exp(exp(5))-3*exp(x**2)*x)*ln(exp(exp 
(5))+x)+12*exp(x**2)*exp(exp(5))+12*exp(x**2)*x)*ln(x/(ln(ln(exp(exp(5))+x 
)-4)+exp(x**2)))+((-9*exp(exp(5))-9*x)*ln(exp(exp(5))+x)+36*exp(exp(5))+36 
*x)*ln(ln(exp(exp(5))+x)-4)+((6*x**2-9)*exp(x**2)*exp(exp(5))+(6*x**3-9*x) 
*exp(x**2))*ln(exp(exp(5))+x)+(-24*x**2+36)*exp(x**2)*exp(exp(5))+(-24*x** 
3+36*x)*exp(x**2)+3*x)/((((x**2*exp(exp(5))+x**3)*ln(exp(exp(5))+x)-4*x**2 
*exp(exp(5))-4*x**3)*ln(ln(exp(exp(5))+x)-4)+(x**2*exp(x**2)*exp(exp(5))+e 
xp(x**2)*x**3)*ln(exp(exp(5))+x)-4*x**2*exp(x**2)*exp(exp(5))-4*exp(x**2)* 
x**3)*ln(x/(ln(ln(exp(exp(5))+x)-4)+exp(x**2)))**2+(((4*x**2*exp(exp(5))+4 
*x**3)*ln(exp(exp(5))+x)-16*x**2*exp(exp(5))-16*x**3)*ln(ln(exp(exp(5))+x) 
-4)+(4*x**2*exp(x**2)*exp(exp(5))+4*exp(x**2)*x**3)*ln(exp(exp(5))+x)-16*x 
**2*exp(x**2)*exp(exp(5))-16*exp(x**2)*x**3)*ln(x/(ln(ln(exp(exp(5))+x)-4) 
+exp(x**2)))+((4*x**2*exp(exp(5))+4*x**3)*ln(exp(exp(5))+x)-16*x**2*exp(ex 
p(5))-16*x**3)*ln(ln(exp(exp(5))+x)-4)+(4*x**2*exp(x**2)*exp(exp(5))+4*exp 
(x**2)*x**3)*ln(exp(exp(5))+x)-16*x**2*exp(x**2)*exp(exp(5))-16*exp(x**2)* 
x**3),x)
 

Output:

Timed out
 

Maxima [A] (verification not implemented)

Time = 0.26 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.97 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \log \left (x\right ) - x \log \left (e^{\left (x^{2}\right )} + \log \left (\log \left (x + e^{\left (e^{5}\right )}\right ) - 4\right )\right ) + 2 \, x} \] Input:

integrate(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)* 
log(log(exp(exp(5))+x)-4)+(-3*exp(x^2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(e 
xp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(5) 
)+x)-4)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5)) 
+36*x)*log(log(exp(exp(5))+x)-4)+((6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9* 
x)*exp(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24*x^3 
+36*x)*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp 
(exp(5))-4*x^3)*log(log(exp(exp(5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*ex 
p(x^2))*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2))*log( 
x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log( 
exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2 
*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp(exp(5))+x)-16*x^2*exp(x^2)*e 
xp(exp(5))-16*x^3*exp(x^2))*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+(( 
4*x^2*exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log 
(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp 
(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2)),x, algorithm="max 
ima")
 

Output:

3/(x*log(x) - x*log(e^(x^2) + log(log(x + e^(e^5)) - 4)) + 2*x)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 1938 vs. \(2 (28) = 56\).

Time = 25.02 (sec) , antiderivative size = 1938, normalized size of antiderivative = 62.52 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\text {Too large to display} \] Input:

integrate(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)* 
log(log(exp(exp(5))+x)-4)+(-3*exp(x^2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(e 
xp(5))+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(5) 
)+x)-4)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5)) 
+36*x)*log(log(exp(exp(5))+x)-4)+((6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9* 
x)*exp(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24*x^3 
+36*x)*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp 
(exp(5))-4*x^3)*log(log(exp(exp(5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+x^3*ex 
p(x^2))*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*x^3*exp(x^2))*log( 
x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log( 
exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2 
*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp(exp(5))+x)-16*x^2*exp(x^2)*e 
xp(exp(5))-16*x^3*exp(x^2))*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+(( 
4*x^2*exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log 
(log(exp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*x^3*exp(x^2))*log(exp 
(exp(5))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*x^3*exp(x^2)),x, algorithm="gia 
c")
 

Output:

3*(2*x^3*e^(x^2)*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4) + 2*x^3*e^(2*x 
^2)*log(x + e^(e^5)) - 8*x^3*e^(x^2)*log(log(x + e^(e^5)) - 4) + 2*x^2*e^( 
x^2 + e^5)*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4) - 8*x^3*e^(2*x^2) + 
2*x^2*e^(2*x^2 + e^5)*log(x + e^(e^5)) - 8*x^2*e^(x^2 + e^5)*log(log(x + e 
^(e^5)) - 4) - 2*x*e^(x^2)*log(x + e^(e^5))*log(log(x + e^(e^5)) - 4) - x* 
log(x + e^(e^5))*log(log(x + e^(e^5)) - 4)^2 - e^(e^5)*log(x + e^(e^5))*lo 
g(log(x + e^(e^5)) - 4)^2 - 8*x^2*e^(2*x^2 + e^5) - x*e^(2*x^2)*log(x + e^ 
(e^5)) + 8*x*e^(x^2)*log(log(x + e^(e^5)) - 4) - 2*e^(x^2 + e^5)*log(x + e 
^(e^5))*log(log(x + e^(e^5)) - 4) + 4*x*log(log(x + e^(e^5)) - 4)^2 + 4*e^ 
(e^5)*log(log(x + e^(e^5)) - 4)^2 + 4*x*e^(2*x^2) + x*e^(x^2) - e^(2*x^2 + 
 e^5)*log(x + e^(e^5)) + x*log(log(x + e^(e^5)) - 4) + 8*e^(x^2 + e^5)*log 
(log(x + e^(e^5)) - 4) + 4*e^(2*x^2 + e^5))/(2*x^4*e^(x^2)*log(x + e^(e^5) 
)*log(x)*log(log(x + e^(e^5)) - 4) - 2*x^4*e^(x^2)*log(x + e^(e^5))*log(e^ 
(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) + 2*x^4*e^(2* 
x^2)*log(x + e^(e^5))*log(x) - 2*x^4*e^(2*x^2)*log(x + e^(e^5))*log(e^(x^2 
) + log(log(x + e^(e^5)) - 4)) + 4*x^4*e^(x^2)*log(x + e^(e^5))*log(log(x 
+ e^(e^5)) - 4) - 8*x^4*e^(x^2)*log(x)*log(log(x + e^(e^5)) - 4) + 2*x^3*e 
^(x^2 + e^5)*log(x + e^(e^5))*log(x)*log(log(x + e^(e^5)) - 4) + 8*x^4*e^( 
x^2)*log(e^(x^2) + log(log(x + e^(e^5)) - 4))*log(log(x + e^(e^5)) - 4) - 
2*x^3*e^(x^2 + e^5)*log(x + e^(e^5))*log(e^(x^2) + log(log(x + e^(e^5))...
 

Mupad [F(-1)]

Timed out. \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx =\text {Too large to display} \] Input:

int(-(3*x + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(12*x*exp(x^ 
2) - log(x + exp(exp(5)))*(3*x*exp(x^2) + 3*exp(x^2)*exp(exp(5))) + 12*exp 
(x^2)*exp(exp(5)) + log(log(x + exp(exp(5))) - 4)*(12*x + 12*exp(exp(5)) - 
 log(x + exp(exp(5)))*(3*x + 3*exp(exp(5))))) + exp(x^2)*(36*x - 24*x^3) + 
 log(log(x + exp(exp(5))) - 4)*(36*x + 36*exp(exp(5)) - log(x + exp(exp(5) 
))*(9*x + 9*exp(exp(5)))) - log(x + exp(exp(5)))*(exp(x^2)*(9*x - 6*x^3) - 
 exp(x^2)*exp(exp(5))*(6*x^2 - 9)) - exp(x^2)*exp(exp(5))*(24*x^2 - 36))/( 
16*x^3*exp(x^2) - log(x + exp(exp(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*ex 
p(exp(5))) + log(log(x + exp(exp(5))) - 4)*(16*x^2*exp(exp(5)) - log(x + e 
xp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + log(x/(exp(x^2) + log( 
log(x + exp(exp(5))) - 4)))*(16*x^3*exp(x^2) - log(x + exp(exp(5)))*(4*x^3 
*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5))) - 4)*(1 
6*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16* 
x^3) + 16*x^2*exp(x^2)*exp(exp(5))) + log(x/(exp(x^2) + log(log(x + exp(ex 
p(5))) - 4)))^2*(4*x^3*exp(x^2) + log(log(x + exp(exp(5))) - 4)*(4*x^2*exp 
(exp(5)) - log(x + exp(exp(5)))*(x^2*exp(exp(5)) + x^3) + 4*x^3) - log(x + 
 exp(exp(5)))*(x^3*exp(x^2) + x^2*exp(x^2)*exp(exp(5))) + 4*x^2*exp(x^2)*e 
xp(exp(5))) + 16*x^2*exp(x^2)*exp(exp(5))),x)
 

Output:

int(-(3*x + log(x/(exp(x^2) + log(log(x + exp(exp(5))) - 4)))*(12*x*exp(x^ 
2) - log(x + exp(exp(5)))*(3*x*exp(x^2) + 3*exp(x^2)*exp(exp(5))) + 12*exp 
(x^2)*exp(exp(5)) + log(log(x + exp(exp(5))) - 4)*(12*x + 12*exp(exp(5)) - 
 log(x + exp(exp(5)))*(3*x + 3*exp(exp(5))))) + exp(x^2)*(36*x - 24*x^3) + 
 log(log(x + exp(exp(5))) - 4)*(36*x + 36*exp(exp(5)) - log(x + exp(exp(5) 
))*(9*x + 9*exp(exp(5)))) - log(x + exp(exp(5)))*(exp(x^2)*(9*x - 6*x^3) - 
 exp(x^2)*exp(exp(5))*(6*x^2 - 9)) - exp(x^2)*exp(exp(5))*(24*x^2 - 36))/( 
16*x^3*exp(x^2) - log(x + exp(exp(5)))*(4*x^3*exp(x^2) + 4*x^2*exp(x^2)*ex 
p(exp(5))) + log(log(x + exp(exp(5))) - 4)*(16*x^2*exp(exp(5)) - log(x + e 
xp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16*x^3) + log(x/(exp(x^2) + log( 
log(x + exp(exp(5))) - 4)))*(16*x^3*exp(x^2) - log(x + exp(exp(5)))*(4*x^3 
*exp(x^2) + 4*x^2*exp(x^2)*exp(exp(5))) + log(log(x + exp(exp(5))) - 4)*(1 
6*x^2*exp(exp(5)) - log(x + exp(exp(5)))*(4*x^2*exp(exp(5)) + 4*x^3) + 16* 
x^3) + 16*x^2*exp(x^2)*exp(exp(5))) + log(x/(exp(x^2) + log(log(x + exp(ex 
p(5))) - 4)))^2*(4*x^3*exp(x^2) + log(log(x + exp(exp(5))) - 4)*(4*x^2*exp 
(exp(5)) - log(x + exp(exp(5)))*(x^2*exp(exp(5)) + x^3) + 4*x^3) - log(x + 
 exp(exp(5)))*(x^3*exp(x^2) + x^2*exp(x^2)*exp(exp(5))) + 4*x^2*exp(x^2)*e 
xp(exp(5))) + 16*x^2*exp(x^2)*exp(exp(5))), x)
 

Reduce [B] (verification not implemented)

Time = 0.34 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.00 \[ \int \frac {3 x+e^{e^5+x^2} \left (36-24 x^2\right )+e^{x^2} \left (36 x-24 x^3\right )+\left (e^{e^5+x^2} \left (-9+6 x^2\right )+e^{x^2} \left (-9 x+6 x^3\right )\right ) \log \left (e^{e^5}+x\right )+\left (36 e^{e^5}+36 x+\left (-9 e^{e^5}-9 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (12 e^{e^5+x^2}+12 e^{x^2} x+\left (-3 e^{e^5+x^2}-3 e^{x^2} x\right ) \log \left (e^{e^5}+x\right )+\left (12 e^{e^5}+12 x+\left (-3 e^{e^5}-3 x\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )}{-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )+\left (-16 e^{e^5+x^2} x^2-16 e^{x^2} x^3+\left (4 e^{e^5+x^2} x^2+4 e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-16 e^{e^5} x^2-16 x^3+\left (4 e^{e^5} x^2+4 x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log \left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )+\left (-4 e^{e^5+x^2} x^2-4 e^{x^2} x^3+\left (e^{e^5+x^2} x^2+e^{x^2} x^3\right ) \log \left (e^{e^5}+x\right )+\left (-4 e^{e^5} x^2-4 x^3+\left (e^{e^5} x^2+x^3\right ) \log \left (e^{e^5}+x\right )\right ) \log \left (-4+\log \left (e^{e^5}+x\right )\right )\right ) \log ^2\left (\frac {x}{e^{x^2}+\log \left (-4+\log \left (e^{e^5}+x\right )\right )}\right )} \, dx=\frac {3}{x \left (\mathrm {log}\left (\frac {x}{e^{x^{2}}+\mathrm {log}\left (\mathrm {log}\left (e^{e^{5}}+x \right )-4\right )}\right )+2\right )} \] Input:

int(((((-3*exp(exp(5))-3*x)*log(exp(exp(5))+x)+12*exp(exp(5))+12*x)*log(lo 
g(exp(exp(5))+x)-4)+(-3*exp(x^2)*exp(exp(5))-3*exp(x^2)*x)*log(exp(exp(5)) 
+x)+12*exp(x^2)*exp(exp(5))+12*exp(x^2)*x)*log(x/(log(log(exp(exp(5))+x)-4 
)+exp(x^2)))+((-9*exp(exp(5))-9*x)*log(exp(exp(5))+x)+36*exp(exp(5))+36*x) 
*log(log(exp(exp(5))+x)-4)+((6*x^2-9)*exp(x^2)*exp(exp(5))+(6*x^3-9*x)*exp 
(x^2))*log(exp(exp(5))+x)+(-24*x^2+36)*exp(x^2)*exp(exp(5))+(-24*x^3+36*x) 
*exp(x^2)+3*x)/((((x^2*exp(exp(5))+x^3)*log(exp(exp(5))+x)-4*x^2*exp(exp(5 
))-4*x^3)*log(log(exp(exp(5))+x)-4)+(x^2*exp(x^2)*exp(exp(5))+exp(x^2)*x^3 
)*log(exp(exp(5))+x)-4*x^2*exp(x^2)*exp(exp(5))-4*exp(x^2)*x^3)*log(x/(log 
(log(exp(exp(5))+x)-4)+exp(x^2)))^2+(((4*x^2*exp(exp(5))+4*x^3)*log(exp(ex 
p(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(exp(exp(5))+x)-4)+(4*x^2*exp(x 
^2)*exp(exp(5))+4*exp(x^2)*x^3)*log(exp(exp(5))+x)-16*x^2*exp(x^2)*exp(exp 
(5))-16*exp(x^2)*x^3)*log(x/(log(log(exp(exp(5))+x)-4)+exp(x^2)))+((4*x^2* 
exp(exp(5))+4*x^3)*log(exp(exp(5))+x)-16*x^2*exp(exp(5))-16*x^3)*log(log(e 
xp(exp(5))+x)-4)+(4*x^2*exp(x^2)*exp(exp(5))+4*exp(x^2)*x^3)*log(exp(exp(5 
))+x)-16*x^2*exp(x^2)*exp(exp(5))-16*exp(x^2)*x^3),x)
 

Output:

3/(x*(log(x/(e**(x**2) + log(log(e**(e**5) + x) - 4))) + 2))