\(\int \frac {-400 x^2+800 x^3-400 x^4+(800 x-1600 x^2+800 x^3) \log (-1+x)+(-400+800 x-400 x^2) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+(-x+x^2) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} (200 x^2-400 x^4+200 x^5+(200 x-400 x^2+800 x^3-400 x^4) \log (-1+x)+(200 x-400 x^2+200 x^3) \log ^2(-1+x))}{e^{\frac {3 (-x+x^2-x^3+(-x+x^2) \log (-1+x))}{x-x^2+(-1+x) \log (-1+x)}} (x^3-2 x^4+x^5+(-2 x^2+4 x^3-2 x^4) \log (-1+x)+(x-2 x^2+x^3) \log ^2(-1+x))+e^{\frac {2 (-x+x^2-x^3+(-x+x^2) \log (-1+x))}{x-x^2+(-1+x) \log (-1+x)}} (-3 x^3+6 x^4-3 x^5+(6 x^2-12 x^3+6 x^4) \log (-1+x)+(-3 x+6 x^2-3 x^3) \log ^2(-1+x)) \log (x^2)+e^{\frac {-x+x^2-x^3+(-x+x^2) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} (3 x^3-6 x^4+3 x^5+(-6 x^2+12 x^3-6 x^4) \log (-1+x)+(3 x-6 x^2+3 x^3) \log ^2(-1+x)) \log ^2(x^2)+(-x^3+2 x^4-x^5+(2 x^2-4 x^3+2 x^4) \log (-1+x)+(-x+2 x^2-x^3) \log ^2(-1+x)) \log ^3(x^2)} \, dx\) [2346]

Optimal result

Integrand size = 540, antiderivative size = 34 \[ \int \frac {-400 x^2+800 x^3-400 x^4+\left (800 x-1600 x^2+800 x^3\right ) \log (-1+x)+\left (-400+800 x-400 x^2\right ) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (200 x^2-400 x^4+200 x^5+\left (200 x-400 x^2+800 x^3-400 x^4\right ) \log (-1+x)+\left (200 x-400 x^2+200 x^3\right ) \log ^2(-1+x)\right )}{e^{\frac {3 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (x^3-2 x^4+x^5+\left (-2 x^2+4 x^3-2 x^4\right ) \log (-1+x)+\left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )+e^{\frac {2 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (-3 x^3+6 x^4-3 x^5+\left (6 x^2-12 x^3+6 x^4\right ) \log (-1+x)+\left (-3 x+6 x^2-3 x^3\right ) \log ^2(-1+x)\right ) \log \left (x^2\right )+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (3 x^3-6 x^4+3 x^5+\left (-6 x^2+12 x^3-6 x^4\right ) \log (-1+x)+\left (3 x-6 x^2+3 x^3\right ) \log ^2(-1+x)\right ) \log ^2\left (x^2\right )+\left (-x^3+2 x^4-x^5+\left (2 x^2-4 x^3+2 x^4\right ) \log (-1+x)+\left (-x+2 x^2-x^3\right ) \log ^2(-1+x)\right ) \log ^3\left (x^2\right )} \, dx=1-\frac {100}{\left (-e^{x+\frac {x}{(-1+x) (x-\log (-1+x))}}+\log \left (x^2\right )\right )^2} \] Output:

1-4/(1/5*ln(x^2)-1/5*exp(x/(x-ln(-1+x))/(-1+x)+x))^2
 

Mathematica [A] (verified)

Time = 0.67 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.38 \[ \int \frac {-400 x^2+800 x^3-400 x^4+\left (800 x-1600 x^2+800 x^3\right ) \log (-1+x)+\left (-400+800 x-400 x^2\right ) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (200 x^2-400 x^4+200 x^5+\left (200 x-400 x^2+800 x^3-400 x^4\right ) \log (-1+x)+\left (200 x-400 x^2+200 x^3\right ) \log ^2(-1+x)\right )}{e^{\frac {3 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (x^3-2 x^4+x^5+\left (-2 x^2+4 x^3-2 x^4\right ) \log (-1+x)+\left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )+e^{\frac {2 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (-3 x^3+6 x^4-3 x^5+\left (6 x^2-12 x^3+6 x^4\right ) \log (-1+x)+\left (-3 x+6 x^2-3 x^3\right ) \log ^2(-1+x)\right ) \log \left (x^2\right )+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (3 x^3-6 x^4+3 x^5+\left (-6 x^2+12 x^3-6 x^4\right ) \log (-1+x)+\left (3 x-6 x^2+3 x^3\right ) \log ^2(-1+x)\right ) \log ^2\left (x^2\right )+\left (-x^3+2 x^4-x^5+\left (2 x^2-4 x^3+2 x^4\right ) \log (-1+x)+\left (-x+2 x^2-x^3\right ) \log ^2(-1+x)\right ) \log ^3\left (x^2\right )} \, dx=-\frac {100}{\left (e^{\frac {x \left (1-x+x^2-(-1+x) \log (-1+x)\right )}{(-1+x) (x-\log (-1+x))}}-\log \left (x^2\right )\right )^2} \] Input:

Integrate[(-400*x^2 + 800*x^3 - 400*x^4 + (800*x - 1600*x^2 + 800*x^3)*Log 
[-1 + x] + (-400 + 800*x - 400*x^2)*Log[-1 + x]^2 + E^((-x + x^2 - x^3 + ( 
-x + x^2)*Log[-1 + x])/(x - x^2 + (-1 + x)*Log[-1 + x]))*(200*x^2 - 400*x^ 
4 + 200*x^5 + (200*x - 400*x^2 + 800*x^3 - 400*x^4)*Log[-1 + x] + (200*x - 
 400*x^2 + 200*x^3)*Log[-1 + x]^2))/(E^((3*(-x + x^2 - x^3 + (-x + x^2)*Lo 
g[-1 + x]))/(x - x^2 + (-1 + x)*Log[-1 + x]))*(x^3 - 2*x^4 + x^5 + (-2*x^2 
 + 4*x^3 - 2*x^4)*Log[-1 + x] + (x - 2*x^2 + x^3)*Log[-1 + x]^2) + E^((2*( 
-x + x^2 - x^3 + (-x + x^2)*Log[-1 + x]))/(x - x^2 + (-1 + x)*Log[-1 + x]) 
)*(-3*x^3 + 6*x^4 - 3*x^5 + (6*x^2 - 12*x^3 + 6*x^4)*Log[-1 + x] + (-3*x + 
 6*x^2 - 3*x^3)*Log[-1 + x]^2)*Log[x^2] + E^((-x + x^2 - x^3 + (-x + x^2)* 
Log[-1 + x])/(x - x^2 + (-1 + x)*Log[-1 + x]))*(3*x^3 - 6*x^4 + 3*x^5 + (- 
6*x^2 + 12*x^3 - 6*x^4)*Log[-1 + x] + (3*x - 6*x^2 + 3*x^3)*Log[-1 + x]^2) 
*Log[x^2]^2 + (-x^3 + 2*x^4 - x^5 + (2*x^2 - 4*x^3 + 2*x^4)*Log[-1 + x] + 
(-x + 2*x^2 - x^3)*Log[-1 + x]^2)*Log[x^2]^3),x]
 

Output:

-100/(E^((x*(1 - x + x^2 - (-1 + x)*Log[-1 + x]))/((-1 + x)*(x - Log[-1 + 
x]))) - Log[x^2])^2
 

Rubi [F]

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.

\(\displaystyle \int \frac {\left (200 x^5-400 x^4+200 x^2+\left (200 x^3-400 x^2+200 x\right ) \log ^2(x-1)+\left (-400 x^4+800 x^3-400 x^2+200 x\right ) \log (x-1)\right ) \exp \left (\frac {-x^3+x^2+\left (x^2-x\right ) \log (x-1)-x}{-x^2+x+(x-1) \log (x-1)}\right )-400 x^4+800 x^3-400 x^2+\left (-400 x^2+800 x-400\right ) \log ^2(x-1)+\left (800 x^3-1600 x^2+800 x\right ) \log (x-1)}{\left (3 x^5-6 x^4+3 x^3+\left (3 x^3-6 x^2+3 x\right ) \log ^2(x-1)+\left (-6 x^4+12 x^3-6 x^2\right ) \log (x-1)\right ) \log ^2\left (x^2\right ) \exp \left (\frac {-x^3+x^2+\left (x^2-x\right ) \log (x-1)-x}{-x^2+x+(x-1) \log (x-1)}\right )+\left (-3 x^5+6 x^4-3 x^3+\left (-3 x^3+6 x^2-3 x\right ) \log ^2(x-1)+\left (6 x^4-12 x^3+6 x^2\right ) \log (x-1)\right ) \log \left (x^2\right ) \exp \left (\frac {2 \left (-x^3+x^2+\left (x^2-x\right ) \log (x-1)-x\right )}{-x^2+x+(x-1) \log (x-1)}\right )+\left (x^5-2 x^4+x^3+\left (x^3-2 x^2+x\right ) \log ^2(x-1)+\left (-2 x^4+4 x^3-2 x^2\right ) \log (x-1)\right ) \exp \left (\frac {3 \left (-x^3+x^2+\left (x^2-x\right ) \log (x-1)-x\right )}{-x^2+x+(x-1) \log (x-1)}\right )+\left (-x^5+2 x^4-x^3+\left (-x^3+2 x^2-x\right ) \log ^2(x-1)+\left (2 x^4-4 x^3+2 x^2\right ) \log (x-1)\right ) \log ^3\left (x^2\right )} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {200 \left (-2 x^4+4 x^3-2 x^2+x e^{\frac {x \left (x^2-x+1\right )}{(x-1) (x-\log (x-1))}} \left (x^4-2 x^3+\left (-2 x^3+4 x^2-2 x+1\right ) \log (x-1)+x+(x-1)^2 \log ^2(x-1)\right ) (x-1)^{-\frac {x}{x-\log (x-1)}}-2 (x-1)^2 \log ^2(x-1)+4 x (x-1)^2 \log (x-1)\right ) \exp \left (-\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}\right )}{(1-x)^2 x (x-\log (x-1))^2 \left (e^{\frac {x^2}{-x^2+x+(x-1) \log (x-1)}} (x-1)^{-\frac {x}{x-\log (x-1)}}-e^{-\frac {x^3+x}{(x-1) (x-\log (x-1))}} \log \left (x^2\right )\right )^3}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 200 \int -\frac {e^{\frac {3 x \left (x^2+1\right )}{(1-x) (x-\log (x-1))}} \left (-\exp \left (-\frac {x \left (x^2-x+1\right )}{(1-x) (x-\log (x-1))}\right ) x \left (x^4-2 x^3+x+(1-x)^2 \log ^2(x-1)+\left (-2 x^3+4 x^2-2 x+1\right ) \log (x-1)\right ) (x-1)^{-\frac {x}{x-\log (x-1)}}+2 x^4-4 x^3+2 x^2+2 (1-x)^2 \log ^2(x-1)-4 (1-x)^2 x \log (x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \left (e^{\frac {x^2}{-x^2+x-(1-x) \log (x-1)}} (x-1)^{-\frac {x}{x-\log (x-1)}}-e^{\frac {x^3+x}{(1-x) (x-\log (x-1))}} \log \left (x^2\right )\right )^3}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -200 \int \frac {e^{\frac {3 x \left (x^2+1\right )}{(1-x) (x-\log (x-1))}} \left (-\exp \left (-\frac {x \left (x^2-x+1\right )}{(1-x) (x-\log (x-1))}\right ) x \left (x^4-2 x^3+x+(1-x)^2 \log ^2(x-1)+\left (-2 x^3+4 x^2-2 x+1\right ) \log (x-1)\right ) (x-1)^{-\frac {x}{x-\log (x-1)}}+2 x^4-4 x^3+2 x^2+2 (1-x)^2 \log ^2(x-1)-4 (1-x)^2 x \log (x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \left (e^{\frac {x^2}{-x^2+x-(1-x) \log (x-1)}} (x-1)^{-\frac {x}{x-\log (x-1)}}-e^{\frac {x^3+x}{(1-x) (x-\log (x-1))}} \log \left (x^2\right )\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {3 x \left (x^2+1\right )}{(1-x) (x-\log (x-1))}+\frac {6 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+2 x^4-4 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-4 x^3+2 \log ^2(x-1) x^2+8 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+2 x^2-4 \log ^2(x-1) x-4 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+2 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(1-x) (x-\log (x-1))}+\frac {4 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {3 x \left (x^2+1\right )}{(1-x) (x-\log (x-1))}+\frac {5 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {2 e^{\frac {3 x \left (x^2+1\right )}{(1-x) (x-\log (x-1))}+\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}}}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -200 \int \frac {-\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-2 x+\left (x^2-x-1\right ) \log \left (x^2\right )+2\right ) x^2+\log (x-1) \left (4 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-2\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^3}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-3 x+\left (x^2-x-1\right ) \log \left (x^2\right )+3\right ) x^2+\log (x-1) \left (6 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-3\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )^2}-\frac {e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}} \left ((x-1) \left (-6 x+\left (x^2-x-1\right ) \log \left (x^2\right )+6\right ) x^2+\log (x-1) \left (12 (x-1)^2+\left (-2 x^3+4 x^2-2 x+1\right ) \log \left (x^2\right )\right ) x+(x-1)^2 \log ^2(x-1) \left (x \log \left (x^2\right )-6\right )\right )}{(x-1)^2 (x-\log (x-1))^2 \left (e^{\frac {x^3+x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}-2}{x \log ^3\left (x^2\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -200 \int \left (\frac {e^{\frac {x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (-\log \left (x^2\right ) x^5+2 \log (x-1) \log \left (x^2\right ) x^4+2 \log \left (x^2\right ) x^4+6 x^4-12 \log (x-1) x^3-\log ^2(x-1) \log \left (x^2\right ) x^3-4 \log (x-1) \log \left (x^2\right ) x^3-12 x^3+6 \log ^2(x-1) x^2+24 \log (x-1) x^2+2 \log ^2(x-1) \log \left (x^2\right ) x^2+2 \log (x-1) \log \left (x^2\right ) x^2-\log \left (x^2\right ) x^2+6 x^2-12 \log ^2(x-1) x-12 \log (x-1) x-\log ^2(x-1) \log \left (x^2\right ) x-\log (x-1) \log \left (x^2\right ) x+6 \log ^2(x-1)\right )}{(1-x)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}-e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )\right )}+\frac {2 e^{\frac {2 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-3 x^4+6 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+6 x^3-3 \log ^2(x-1) x^2-12 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-3 x^2+6 \log ^2(x-1) x+6 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-3 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^2}+\frac {e^{\frac {3 x \left (x^2+1\right )}{(x-1) (x-\log (x-1))}} \left (\log \left (x^2\right ) x^5-2 \log (x-1) \log \left (x^2\right ) x^4-2 \log \left (x^2\right ) x^4-2 x^4+4 \log (x-1) x^3+\log ^2(x-1) \log \left (x^2\right ) x^3+4 \log (x-1) \log \left (x^2\right ) x^3+4 x^3-2 \log ^2(x-1) x^2-8 \log (x-1) x^2-2 \log ^2(x-1) \log \left (x^2\right ) x^2-2 \log (x-1) \log \left (x^2\right ) x^2+\log \left (x^2\right ) x^2-2 x^2+4 \log ^2(x-1) x+4 \log (x-1) x+\log ^2(x-1) \log \left (x^2\right ) x+\log (x-1) \log \left (x^2\right ) x-2 \log ^2(x-1)\right )}{(x-1)^2 x (x-\log (x-1))^2 \log ^3\left (x^2\right ) \left (e^{\frac {x^2}{(x-1) (x-\log (x-1))}} (x-1)^{\frac {x}{x-\log (x-1)}} \log \left (x^2\right )-e^{\frac {x^3}{(x-1) (x-\log (x-1))}+\frac {x}{(x-1) (x-\log (x-1))}}\right )^3}-\frac {2}{x \log ^3\left (x^2\right )}\right )dx\)

Input:

Int[(-400*x^2 + 800*x^3 - 400*x^4 + (800*x - 1600*x^2 + 800*x^3)*Log[-1 + 
x] + (-400 + 800*x - 400*x^2)*Log[-1 + x]^2 + E^((-x + x^2 - x^3 + (-x + x 
^2)*Log[-1 + x])/(x - x^2 + (-1 + x)*Log[-1 + x]))*(200*x^2 - 400*x^4 + 20 
0*x^5 + (200*x - 400*x^2 + 800*x^3 - 400*x^4)*Log[-1 + x] + (200*x - 400*x 
^2 + 200*x^3)*Log[-1 + x]^2))/(E^((3*(-x + x^2 - x^3 + (-x + x^2)*Log[-1 + 
 x]))/(x - x^2 + (-1 + x)*Log[-1 + x]))*(x^3 - 2*x^4 + x^5 + (-2*x^2 + 4*x 
^3 - 2*x^4)*Log[-1 + x] + (x - 2*x^2 + x^3)*Log[-1 + x]^2) + E^((2*(-x + x 
^2 - x^3 + (-x + x^2)*Log[-1 + x]))/(x - x^2 + (-1 + x)*Log[-1 + x]))*(-3* 
x^3 + 6*x^4 - 3*x^5 + (6*x^2 - 12*x^3 + 6*x^4)*Log[-1 + x] + (-3*x + 6*x^2 
 - 3*x^3)*Log[-1 + x]^2)*Log[x^2] + E^((-x + x^2 - x^3 + (-x + x^2)*Log[-1 
 + x])/(x - x^2 + (-1 + x)*Log[-1 + x]))*(3*x^3 - 6*x^4 + 3*x^5 + (-6*x^2 
+ 12*x^3 - 6*x^4)*Log[-1 + x] + (3*x - 6*x^2 + 3*x^3)*Log[-1 + x]^2)*Log[x 
^2]^2 + (-x^3 + 2*x^4 - x^5 + (2*x^2 - 4*x^3 + 2*x^4)*Log[-1 + x] + (-x + 
2*x^2 - x^3)*Log[-1 + x]^2)*Log[x^2]^3),x]
 

Output:

$Aborted
 

Maple [F(-1)]

Timed out.

\[\int \frac {\left (\left (200 x^{3}-400 x^{2}+200 x \right ) \ln \left (-1+x \right )^{2}+\left (-400 x^{4}+800 x^{3}-400 x^{2}+200 x \right ) \ln \left (-1+x \right )+200 x^{5}-400 x^{4}+200 x^{2}\right ) {\mathrm e}^{\frac {\left (x^{2}-x \right ) \ln \left (-1+x \right )-x^{3}+x^{2}-x}{\left (-1+x \right ) \ln \left (-1+x \right )-x^{2}+x}}+\left (-400 x^{2}+800 x -400\right ) \ln \left (-1+x \right )^{2}+\left (800 x^{3}-1600 x^{2}+800 x \right ) \ln \left (-1+x \right )-400 x^{4}+800 x^{3}-400 x^{2}}{\left (\left (x^{3}-2 x^{2}+x \right ) \ln \left (-1+x \right )^{2}+\left (-2 x^{4}+4 x^{3}-2 x^{2}\right ) \ln \left (-1+x \right )+x^{5}-2 x^{4}+x^{3}\right ) {\mathrm e}^{\frac {3 \left (x^{2}-x \right ) \ln \left (-1+x \right )-3 x^{3}+3 x^{2}-3 x}{\left (-1+x \right ) \ln \left (-1+x \right )-x^{2}+x}}+\left (\left (-3 x^{3}+6 x^{2}-3 x \right ) \ln \left (-1+x \right )^{2}+\left (6 x^{4}-12 x^{3}+6 x^{2}\right ) \ln \left (-1+x \right )-3 x^{5}+6 x^{4}-3 x^{3}\right ) \ln \left (x^{2}\right ) {\mathrm e}^{\frac {2 \left (x^{2}-x \right ) \ln \left (-1+x \right )-2 x^{3}+2 x^{2}-2 x}{\left (-1+x \right ) \ln \left (-1+x \right )-x^{2}+x}}+\left (\left (3 x^{3}-6 x^{2}+3 x \right ) \ln \left (-1+x \right )^{2}+\left (-6 x^{4}+12 x^{3}-6 x^{2}\right ) \ln \left (-1+x \right )+3 x^{5}-6 x^{4}+3 x^{3}\right ) \ln \left (x^{2}\right )^{2} {\mathrm e}^{\frac {\left (x^{2}-x \right ) \ln \left (-1+x \right )-x^{3}+x^{2}-x}{\left (-1+x \right ) \ln \left (-1+x \right )-x^{2}+x}}+\left (\left (-x^{3}+2 x^{2}-x \right ) \ln \left (-1+x \right )^{2}+\left (2 x^{4}-4 x^{3}+2 x^{2}\right ) \ln \left (-1+x \right )-x^{5}+2 x^{4}-x^{3}\right ) \ln \left (x^{2}\right )^{3}}d x\]

Input:

int((((200*x^3-400*x^2+200*x)*ln(-1+x)^2+(-400*x^4+800*x^3-400*x^2+200*x)* 
ln(-1+x)+200*x^5-400*x^4+200*x^2)*exp(((x^2-x)*ln(-1+x)-x^3+x^2-x)/((-1+x) 
*ln(-1+x)-x^2+x))+(-400*x^2+800*x-400)*ln(-1+x)^2+(800*x^3-1600*x^2+800*x) 
*ln(-1+x)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*ln(-1+x)^2+(-2*x^4+4*x^ 
3-2*x^2)*ln(-1+x)+x^5-2*x^4+x^3)*exp(((x^2-x)*ln(-1+x)-x^3+x^2-x)/((-1+x)* 
ln(-1+x)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*ln(-1+x)^2+(6*x^4-12*x^3+6*x^2)*ln( 
-1+x)-3*x^5+6*x^4-3*x^3)*ln(x^2)*exp(((x^2-x)*ln(-1+x)-x^3+x^2-x)/((-1+x)* 
ln(-1+x)-x^2+x))^2+((3*x^3-6*x^2+3*x)*ln(-1+x)^2+(-6*x^4+12*x^3-6*x^2)*ln( 
-1+x)+3*x^5-6*x^4+3*x^3)*ln(x^2)^2*exp(((x^2-x)*ln(-1+x)-x^3+x^2-x)/((-1+x 
)*ln(-1+x)-x^2+x))+((-x^3+2*x^2-x)*ln(-1+x)^2+(2*x^4-4*x^3+2*x^2)*ln(-1+x) 
-x^5+2*x^4-x^3)*ln(x^2)^3),x)
 

Output:

int((((200*x^3-400*x^2+200*x)*ln(-1+x)^2+(-400*x^4+800*x^3-400*x^2+200*x)* 
ln(-1+x)+200*x^5-400*x^4+200*x^2)*exp(((x^2-x)*ln(-1+x)-x^3+x^2-x)/((-1+x) 
*ln(-1+x)-x^2+x))+(-400*x^2+800*x-400)*ln(-1+x)^2+(800*x^3-1600*x^2+800*x) 
*ln(-1+x)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*ln(-1+x)^2+(-2*x^4+4*x^ 
3-2*x^2)*ln(-1+x)+x^5-2*x^4+x^3)*exp(((x^2-x)*ln(-1+x)-x^3+x^2-x)/((-1+x)* 
ln(-1+x)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*ln(-1+x)^2+(6*x^4-12*x^3+6*x^2)*ln( 
-1+x)-3*x^5+6*x^4-3*x^3)*ln(x^2)*exp(((x^2-x)*ln(-1+x)-x^3+x^2-x)/((-1+x)* 
ln(-1+x)-x^2+x))^2+((3*x^3-6*x^2+3*x)*ln(-1+x)^2+(-6*x^4+12*x^3-6*x^2)*ln( 
-1+x)+3*x^5-6*x^4+3*x^3)*ln(x^2)^2*exp(((x^2-x)*ln(-1+x)-x^3+x^2-x)/((-1+x 
)*ln(-1+x)-x^2+x))+((-x^3+2*x^2-x)*ln(-1+x)^2+(2*x^4-4*x^3+2*x^2)*ln(-1+x) 
-x^5+2*x^4-x^3)*ln(x^2)^3),x)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (33) = 66\).

Time = 0.11 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.18 \[ \int \frac {-400 x^2+800 x^3-400 x^4+\left (800 x-1600 x^2+800 x^3\right ) \log (-1+x)+\left (-400+800 x-400 x^2\right ) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (200 x^2-400 x^4+200 x^5+\left (200 x-400 x^2+800 x^3-400 x^4\right ) \log (-1+x)+\left (200 x-400 x^2+200 x^3\right ) \log ^2(-1+x)\right )}{e^{\frac {3 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (x^3-2 x^4+x^5+\left (-2 x^2+4 x^3-2 x^4\right ) \log (-1+x)+\left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )+e^{\frac {2 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (-3 x^3+6 x^4-3 x^5+\left (6 x^2-12 x^3+6 x^4\right ) \log (-1+x)+\left (-3 x+6 x^2-3 x^3\right ) \log ^2(-1+x)\right ) \log \left (x^2\right )+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (3 x^3-6 x^4+3 x^5+\left (-6 x^2+12 x^3-6 x^4\right ) \log (-1+x)+\left (3 x-6 x^2+3 x^3\right ) \log ^2(-1+x)\right ) \log ^2\left (x^2\right )+\left (-x^3+2 x^4-x^5+\left (2 x^2-4 x^3+2 x^4\right ) \log (-1+x)+\left (-x+2 x^2-x^3\right ) \log ^2(-1+x)\right ) \log ^3\left (x^2\right )} \, dx=\frac {100}{2 \, e^{\left (\frac {x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (x - 1\right ) + x}{x^{2} - {\left (x - 1\right )} \log \left (x - 1\right ) - x}\right )} \log \left (x^{2}\right ) - \log \left (x^{2}\right )^{2} - e^{\left (\frac {2 \, {\left (x^{3} - x^{2} - {\left (x^{2} - x\right )} \log \left (x - 1\right ) + x\right )}}{x^{2} - {\left (x - 1\right )} \log \left (x - 1\right ) - x}\right )}} \] Input:

integrate((((200*x^3-400*x^2+200*x)*log(-1+x)^2+(-400*x^4+800*x^3-400*x^2+ 
200*x)*log(-1+x)+200*x^5-400*x^4+200*x^2)*exp(((x^2-x)*log(-1+x)-x^3+x^2-x 
)/((-1+x)*log(-1+x)-x^2+x))+(-400*x^2+800*x-400)*log(-1+x)^2+(800*x^3-1600 
*x^2+800*x)*log(-1+x)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*log(-1+x)^2 
+(-2*x^4+4*x^3-2*x^2)*log(-1+x)+x^5-2*x^4+x^3)*exp(((x^2-x)*log(-1+x)-x^3+ 
x^2-x)/((-1+x)*log(-1+x)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*log(-1+x)^2+(6*x^4- 
12*x^3+6*x^2)*log(-1+x)-3*x^5+6*x^4-3*x^3)*log(x^2)*exp(((x^2-x)*log(-1+x) 
-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))^2+((3*x^3-6*x^2+3*x)*log(-1+x)^2+(-6 
*x^4+12*x^3-6*x^2)*log(-1+x)+3*x^5-6*x^4+3*x^3)*log(x^2)^2*exp(((x^2-x)*lo 
g(-1+x)-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))+((-x^3+2*x^2-x)*log(-1+x)^2+( 
2*x^4-4*x^3+2*x^2)*log(-1+x)-x^5+2*x^4-x^3)*log(x^2)^3),x, algorithm="fric 
as")
 

Output:

100/(2*e^((x^3 - x^2 - (x^2 - x)*log(x - 1) + x)/(x^2 - (x - 1)*log(x - 1) 
 - x))*log(x^2) - log(x^2)^2 - e^(2*(x^3 - x^2 - (x^2 - x)*log(x - 1) + x) 
/(x^2 - (x - 1)*log(x - 1) - x)))
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 90 vs. \(2 (27) = 54\).

Time = 1.85 (sec) , antiderivative size = 90, normalized size of antiderivative = 2.65 \[ \int \frac {-400 x^2+800 x^3-400 x^4+\left (800 x-1600 x^2+800 x^3\right ) \log (-1+x)+\left (-400+800 x-400 x^2\right ) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (200 x^2-400 x^4+200 x^5+\left (200 x-400 x^2+800 x^3-400 x^4\right ) \log (-1+x)+\left (200 x-400 x^2+200 x^3\right ) \log ^2(-1+x)\right )}{e^{\frac {3 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (x^3-2 x^4+x^5+\left (-2 x^2+4 x^3-2 x^4\right ) \log (-1+x)+\left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )+e^{\frac {2 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (-3 x^3+6 x^4-3 x^5+\left (6 x^2-12 x^3+6 x^4\right ) \log (-1+x)+\left (-3 x+6 x^2-3 x^3\right ) \log ^2(-1+x)\right ) \log \left (x^2\right )+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (3 x^3-6 x^4+3 x^5+\left (-6 x^2+12 x^3-6 x^4\right ) \log (-1+x)+\left (3 x-6 x^2+3 x^3\right ) \log ^2(-1+x)\right ) \log ^2\left (x^2\right )+\left (-x^3+2 x^4-x^5+\left (2 x^2-4 x^3+2 x^4\right ) \log (-1+x)+\left (-x+2 x^2-x^3\right ) \log ^2(-1+x)\right ) \log ^3\left (x^2\right )} \, dx=- \frac {100}{e^{\frac {2 \left (- x^{3} + x^{2} - x + \left (x^{2} - x\right ) \log {\left (x - 1 \right )}\right )}{- x^{2} + x + \left (x - 1\right ) \log {\left (x - 1 \right )}}} - 2 e^{\frac {- x^{3} + x^{2} - x + \left (x^{2} - x\right ) \log {\left (x - 1 \right )}}{- x^{2} + x + \left (x - 1\right ) \log {\left (x - 1 \right )}}} \log {\left (x^{2} \right )} + \log {\left (x^{2} \right )}^{2}} \] Input:

integrate((((200*x**3-400*x**2+200*x)*ln(-1+x)**2+(-400*x**4+800*x**3-400* 
x**2+200*x)*ln(-1+x)+200*x**5-400*x**4+200*x**2)*exp(((x**2-x)*ln(-1+x)-x* 
*3+x**2-x)/((-1+x)*ln(-1+x)-x**2+x))+(-400*x**2+800*x-400)*ln(-1+x)**2+(80 
0*x**3-1600*x**2+800*x)*ln(-1+x)-400*x**4+800*x**3-400*x**2)/(((x**3-2*x** 
2+x)*ln(-1+x)**2+(-2*x**4+4*x**3-2*x**2)*ln(-1+x)+x**5-2*x**4+x**3)*exp((( 
x**2-x)*ln(-1+x)-x**3+x**2-x)/((-1+x)*ln(-1+x)-x**2+x))**3+((-3*x**3+6*x** 
2-3*x)*ln(-1+x)**2+(6*x**4-12*x**3+6*x**2)*ln(-1+x)-3*x**5+6*x**4-3*x**3)* 
ln(x**2)*exp(((x**2-x)*ln(-1+x)-x**3+x**2-x)/((-1+x)*ln(-1+x)-x**2+x))**2+ 
((3*x**3-6*x**2+3*x)*ln(-1+x)**2+(-6*x**4+12*x**3-6*x**2)*ln(-1+x)+3*x**5- 
6*x**4+3*x**3)*ln(x**2)**2*exp(((x**2-x)*ln(-1+x)-x**3+x**2-x)/((-1+x)*ln( 
-1+x)-x**2+x))+((-x**3+2*x**2-x)*ln(-1+x)**2+(2*x**4-4*x**3+2*x**2)*ln(-1+ 
x)-x**5+2*x**4-x**3)*ln(x**2)**3),x)
 

Output:

-100/(exp(2*(-x**3 + x**2 - x + (x**2 - x)*log(x - 1))/(-x**2 + x + (x - 1 
)*log(x - 1))) - 2*exp((-x**3 + x**2 - x + (x**2 - x)*log(x - 1))/(-x**2 + 
 x + (x - 1)*log(x - 1)))*log(x**2) + log(x**2)**2)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 140 vs. \(2 (33) = 66\).

Time = 2.65 (sec) , antiderivative size = 140, normalized size of antiderivative = 4.12 \[ \int \frac {-400 x^2+800 x^3-400 x^4+\left (800 x-1600 x^2+800 x^3\right ) \log (-1+x)+\left (-400+800 x-400 x^2\right ) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (200 x^2-400 x^4+200 x^5+\left (200 x-400 x^2+800 x^3-400 x^4\right ) \log (-1+x)+\left (200 x-400 x^2+200 x^3\right ) \log ^2(-1+x)\right )}{e^{\frac {3 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (x^3-2 x^4+x^5+\left (-2 x^2+4 x^3-2 x^4\right ) \log (-1+x)+\left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )+e^{\frac {2 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (-3 x^3+6 x^4-3 x^5+\left (6 x^2-12 x^3+6 x^4\right ) \log (-1+x)+\left (-3 x+6 x^2-3 x^3\right ) \log ^2(-1+x)\right ) \log \left (x^2\right )+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (3 x^3-6 x^4+3 x^5+\left (-6 x^2+12 x^3-6 x^4\right ) \log (-1+x)+\left (3 x-6 x^2+3 x^3\right ) \log ^2(-1+x)\right ) \log ^2\left (x^2\right )+\left (-x^3+2 x^4-x^5+\left (2 x^2-4 x^3+2 x^4\right ) \log (-1+x)+\left (-x+2 x^2-x^3\right ) \log ^2(-1+x)\right ) \log ^3\left (x^2\right )} \, dx=-\frac {100 \, e^{\left (\frac {2}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right ) + 1}\right )}}{4 \, e^{\left (\frac {2}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right ) + 1}\right )} \log \left (x\right )^{2} - 4 \, e^{\left (x + \frac {\log \left (x - 1\right )}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right )^{2} + \log \left (x - 1\right )} + \frac {1}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right ) + 1}\right )} \log \left (x\right ) + e^{\left (2 \, x + \frac {2 \, \log \left (x - 1\right )}{x {\left (\log \left (x - 1\right ) - 1\right )} - \log \left (x - 1\right )^{2} + \log \left (x - 1\right )}\right )}} \] Input:

integrate((((200*x^3-400*x^2+200*x)*log(-1+x)^2+(-400*x^4+800*x^3-400*x^2+ 
200*x)*log(-1+x)+200*x^5-400*x^4+200*x^2)*exp(((x^2-x)*log(-1+x)-x^3+x^2-x 
)/((-1+x)*log(-1+x)-x^2+x))+(-400*x^2+800*x-400)*log(-1+x)^2+(800*x^3-1600 
*x^2+800*x)*log(-1+x)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*log(-1+x)^2 
+(-2*x^4+4*x^3-2*x^2)*log(-1+x)+x^5-2*x^4+x^3)*exp(((x^2-x)*log(-1+x)-x^3+ 
x^2-x)/((-1+x)*log(-1+x)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*log(-1+x)^2+(6*x^4- 
12*x^3+6*x^2)*log(-1+x)-3*x^5+6*x^4-3*x^3)*log(x^2)*exp(((x^2-x)*log(-1+x) 
-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))^2+((3*x^3-6*x^2+3*x)*log(-1+x)^2+(-6 
*x^4+12*x^3-6*x^2)*log(-1+x)+3*x^5-6*x^4+3*x^3)*log(x^2)^2*exp(((x^2-x)*lo 
g(-1+x)-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))+((-x^3+2*x^2-x)*log(-1+x)^2+( 
2*x^4-4*x^3+2*x^2)*log(-1+x)-x^5+2*x^4-x^3)*log(x^2)^3),x, algorithm="maxi 
ma")
 

Output:

-100*e^(2/(x*(log(x - 1) - 1) - log(x - 1) + 1))/(4*e^(2/(x*(log(x - 1) - 
1) - log(x - 1) + 1))*log(x)^2 - 4*e^(x + log(x - 1)/(x*(log(x - 1) - 1) - 
 log(x - 1)^2 + log(x - 1)) + 1/(x*(log(x - 1) - 1) - log(x - 1) + 1))*log 
(x) + e^(2*x + 2*log(x - 1)/(x*(log(x - 1) - 1) - log(x - 1)^2 + log(x - 1 
))))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (33) = 66\).

Time = 57.27 (sec) , antiderivative size = 116, normalized size of antiderivative = 3.41 \[ \int \frac {-400 x^2+800 x^3-400 x^4+\left (800 x-1600 x^2+800 x^3\right ) \log (-1+x)+\left (-400+800 x-400 x^2\right ) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (200 x^2-400 x^4+200 x^5+\left (200 x-400 x^2+800 x^3-400 x^4\right ) \log (-1+x)+\left (200 x-400 x^2+200 x^3\right ) \log ^2(-1+x)\right )}{e^{\frac {3 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (x^3-2 x^4+x^5+\left (-2 x^2+4 x^3-2 x^4\right ) \log (-1+x)+\left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )+e^{\frac {2 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (-3 x^3+6 x^4-3 x^5+\left (6 x^2-12 x^3+6 x^4\right ) \log (-1+x)+\left (-3 x+6 x^2-3 x^3\right ) \log ^2(-1+x)\right ) \log \left (x^2\right )+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (3 x^3-6 x^4+3 x^5+\left (-6 x^2+12 x^3-6 x^4\right ) \log (-1+x)+\left (3 x-6 x^2+3 x^3\right ) \log ^2(-1+x)\right ) \log ^2\left (x^2\right )+\left (-x^3+2 x^4-x^5+\left (2 x^2-4 x^3+2 x^4\right ) \log (-1+x)+\left (-x+2 x^2-x^3\right ) \log ^2(-1+x)\right ) \log ^3\left (x^2\right )} \, dx=\frac {100}{2 \, e^{\left (\frac {x^{3} - x^{2} \log \left (x - 1\right ) - x^{2} + x \log \left (x - 1\right ) + x}{x^{2} - x \log \left (x - 1\right ) - x + \log \left (x - 1\right )}\right )} \log \left (x^{2}\right ) - \log \left (x^{2}\right )^{2} - e^{\left (\frac {2 \, {\left (x^{3} - x^{2} \log \left (x - 1\right ) - x^{2} + x \log \left (x - 1\right ) + x\right )}}{x^{2} - x \log \left (x - 1\right ) - x + \log \left (x - 1\right )}\right )}} \] Input:

integrate((((200*x^3-400*x^2+200*x)*log(-1+x)^2+(-400*x^4+800*x^3-400*x^2+ 
200*x)*log(-1+x)+200*x^5-400*x^4+200*x^2)*exp(((x^2-x)*log(-1+x)-x^3+x^2-x 
)/((-1+x)*log(-1+x)-x^2+x))+(-400*x^2+800*x-400)*log(-1+x)^2+(800*x^3-1600 
*x^2+800*x)*log(-1+x)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*log(-1+x)^2 
+(-2*x^4+4*x^3-2*x^2)*log(-1+x)+x^5-2*x^4+x^3)*exp(((x^2-x)*log(-1+x)-x^3+ 
x^2-x)/((-1+x)*log(-1+x)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*log(-1+x)^2+(6*x^4- 
12*x^3+6*x^2)*log(-1+x)-3*x^5+6*x^4-3*x^3)*log(x^2)*exp(((x^2-x)*log(-1+x) 
-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))^2+((3*x^3-6*x^2+3*x)*log(-1+x)^2+(-6 
*x^4+12*x^3-6*x^2)*log(-1+x)+3*x^5-6*x^4+3*x^3)*log(x^2)^2*exp(((x^2-x)*lo 
g(-1+x)-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))+((-x^3+2*x^2-x)*log(-1+x)^2+( 
2*x^4-4*x^3+2*x^2)*log(-1+x)-x^5+2*x^4-x^3)*log(x^2)^3),x, algorithm="giac 
")
 

Output:

100/(2*e^((x^3 - x^2*log(x - 1) - x^2 + x*log(x - 1) + x)/(x^2 - x*log(x - 
 1) - x + log(x - 1)))*log(x^2) - log(x^2)^2 - e^(2*(x^3 - x^2*log(x - 1) 
- x^2 + x*log(x - 1) + x)/(x^2 - x*log(x - 1) - x + log(x - 1))))
 

Mupad [B] (verification not implemented)

Time = 3.61 (sec) , antiderivative size = 212, normalized size of antiderivative = 6.24 \[ \int \frac {-400 x^2+800 x^3-400 x^4+\left (800 x-1600 x^2+800 x^3\right ) \log (-1+x)+\left (-400+800 x-400 x^2\right ) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (200 x^2-400 x^4+200 x^5+\left (200 x-400 x^2+800 x^3-400 x^4\right ) \log (-1+x)+\left (200 x-400 x^2+200 x^3\right ) \log ^2(-1+x)\right )}{e^{\frac {3 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (x^3-2 x^4+x^5+\left (-2 x^2+4 x^3-2 x^4\right ) \log (-1+x)+\left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )+e^{\frac {2 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (-3 x^3+6 x^4-3 x^5+\left (6 x^2-12 x^3+6 x^4\right ) \log (-1+x)+\left (-3 x+6 x^2-3 x^3\right ) \log ^2(-1+x)\right ) \log \left (x^2\right )+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (3 x^3-6 x^4+3 x^5+\left (-6 x^2+12 x^3-6 x^4\right ) \log (-1+x)+\left (3 x-6 x^2+3 x^3\right ) \log ^2(-1+x)\right ) \log ^2\left (x^2\right )+\left (-x^3+2 x^4-x^5+\left (2 x^2-4 x^3+2 x^4\right ) \log (-1+x)+\left (-x+2 x^2-x^3\right ) \log ^2(-1+x)\right ) \log ^3\left (x^2\right )} \, dx=-\frac {100}{{\ln \left (x^2\right )}^2+\frac {{\mathrm {e}}^{-\frac {2\,x}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}\,{\mathrm {e}}^{\frac {2\,x^2}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}\,{\mathrm {e}}^{-\frac {2\,x^3}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}}{{\left (x-1\right )}^{\frac {2\,x}{x-\ln \left (x-1\right )}}}-\frac {2\,\ln \left (x^2\right )\,{\mathrm {e}}^{-\frac {x}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}\,{\mathrm {e}}^{\frac {x^2}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}\,{\mathrm {e}}^{-\frac {x^3}{x-\ln \left (x-1\right )+x\,\ln \left (x-1\right )-x^2}}}{{\left (x-1\right )}^{\frac {x}{x-\ln \left (x-1\right )}}}} \] Input:

int((log(x - 1)*(800*x - 1600*x^2 + 800*x^3) - log(x - 1)^2*(400*x^2 - 800 
*x + 400) + exp(-(x + log(x - 1)*(x - x^2) - x^2 + x^3)/(x + log(x - 1)*(x 
 - 1) - x^2))*(log(x - 1)*(200*x - 400*x^2 + 800*x^3 - 400*x^4) + log(x - 
1)^2*(200*x - 400*x^2 + 200*x^3) + 200*x^2 - 400*x^4 + 200*x^5) - 400*x^2 
+ 800*x^3 - 400*x^4)/(exp(-(3*(x + log(x - 1)*(x - x^2) - x^2 + x^3))/(x + 
 log(x - 1)*(x - 1) - x^2))*(x^3 - log(x - 1)*(2*x^2 - 4*x^3 + 2*x^4) - 2* 
x^4 + x^5 + log(x - 1)^2*(x - 2*x^2 + x^3)) - log(x^2)^3*(x^3 - log(x - 1) 
*(2*x^2 - 4*x^3 + 2*x^4) - 2*x^4 + x^5 + log(x - 1)^2*(x - 2*x^2 + x^3)) - 
 log(x^2)*exp(-(2*(x + log(x - 1)*(x - x^2) - x^2 + x^3))/(x + log(x - 1)* 
(x - 1) - x^2))*(log(x - 1)^2*(3*x - 6*x^2 + 3*x^3) - log(x - 1)*(6*x^2 - 
12*x^3 + 6*x^4) + 3*x^3 - 6*x^4 + 3*x^5) + log(x^2)^2*exp(-(x + log(x - 1) 
*(x - x^2) - x^2 + x^3)/(x + log(x - 1)*(x - 1) - x^2))*(log(x - 1)^2*(3*x 
 - 6*x^2 + 3*x^3) - log(x - 1)*(6*x^2 - 12*x^3 + 6*x^4) + 3*x^3 - 6*x^4 + 
3*x^5)),x)
 

Output:

-100/(log(x^2)^2 + (exp(-(2*x)/(x - log(x - 1) + x*log(x - 1) - x^2))*exp( 
(2*x^2)/(x - log(x - 1) + x*log(x - 1) - x^2))*exp(-(2*x^3)/(x - log(x - 1 
) + x*log(x - 1) - x^2)))/(x - 1)^((2*x)/(x - log(x - 1))) - (2*log(x^2)*e 
xp(-x/(x - log(x - 1) + x*log(x - 1) - x^2))*exp(x^2/(x - log(x - 1) + x*l 
og(x - 1) - x^2))*exp(-x^3/(x - log(x - 1) + x*log(x - 1) - x^2)))/(x - 1) 
^(x/(x - log(x - 1))))
 

Reduce [B] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 124, normalized size of antiderivative = 3.65 \[ \int \frac {-400 x^2+800 x^3-400 x^4+\left (800 x-1600 x^2+800 x^3\right ) \log (-1+x)+\left (-400+800 x-400 x^2\right ) \log ^2(-1+x)+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (200 x^2-400 x^4+200 x^5+\left (200 x-400 x^2+800 x^3-400 x^4\right ) \log (-1+x)+\left (200 x-400 x^2+200 x^3\right ) \log ^2(-1+x)\right )}{e^{\frac {3 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (x^3-2 x^4+x^5+\left (-2 x^2+4 x^3-2 x^4\right ) \log (-1+x)+\left (x-2 x^2+x^3\right ) \log ^2(-1+x)\right )+e^{\frac {2 \left (-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)\right )}{x-x^2+(-1+x) \log (-1+x)}} \left (-3 x^3+6 x^4-3 x^5+\left (6 x^2-12 x^3+6 x^4\right ) \log (-1+x)+\left (-3 x+6 x^2-3 x^3\right ) \log ^2(-1+x)\right ) \log \left (x^2\right )+e^{\frac {-x+x^2-x^3+\left (-x+x^2\right ) \log (-1+x)}{x-x^2+(-1+x) \log (-1+x)}} \left (3 x^3-6 x^4+3 x^5+\left (-6 x^2+12 x^3-6 x^4\right ) \log (-1+x)+\left (3 x-6 x^2+3 x^3\right ) \log ^2(-1+x)\right ) \log ^2\left (x^2\right )+\left (-x^3+2 x^4-x^5+\left (2 x^2-4 x^3+2 x^4\right ) \log (-1+x)+\left (-x+2 x^2-x^3\right ) \log ^2(-1+x)\right ) \log ^3\left (x^2\right )} \, dx=-\frac {100 e^{\frac {2 x}{\mathrm {log}\left (x -1\right ) x -\mathrm {log}\left (x -1\right )-x^{2}+x}}}{e^{\frac {2 x}{\mathrm {log}\left (x -1\right ) x -\mathrm {log}\left (x -1\right )-x^{2}+x}} \mathrm {log}\left (x^{2}\right )^{2}-2 e^{\frac {\mathrm {log}\left (x -1\right ) x^{2}-\mathrm {log}\left (x -1\right ) x -x^{3}+x^{2}+x}{\mathrm {log}\left (x -1\right ) x -\mathrm {log}\left (x -1\right )-x^{2}+x}} \mathrm {log}\left (x^{2}\right )+e^{2 x}} \] Input:

int((((200*x^3-400*x^2+200*x)*log(-1+x)^2+(-400*x^4+800*x^3-400*x^2+200*x) 
*log(-1+x)+200*x^5-400*x^4+200*x^2)*exp(((x^2-x)*log(-1+x)-x^3+x^2-x)/((-1 
+x)*log(-1+x)-x^2+x))+(-400*x^2+800*x-400)*log(-1+x)^2+(800*x^3-1600*x^2+8 
00*x)*log(-1+x)-400*x^4+800*x^3-400*x^2)/(((x^3-2*x^2+x)*log(-1+x)^2+(-2*x 
^4+4*x^3-2*x^2)*log(-1+x)+x^5-2*x^4+x^3)*exp(((x^2-x)*log(-1+x)-x^3+x^2-x) 
/((-1+x)*log(-1+x)-x^2+x))^3+((-3*x^3+6*x^2-3*x)*log(-1+x)^2+(6*x^4-12*x^3 
+6*x^2)*log(-1+x)-3*x^5+6*x^4-3*x^3)*log(x^2)*exp(((x^2-x)*log(-1+x)-x^3+x 
^2-x)/((-1+x)*log(-1+x)-x^2+x))^2+((3*x^3-6*x^2+3*x)*log(-1+x)^2+(-6*x^4+1 
2*x^3-6*x^2)*log(-1+x)+3*x^5-6*x^4+3*x^3)*log(x^2)^2*exp(((x^2-x)*log(-1+x 
)-x^3+x^2-x)/((-1+x)*log(-1+x)-x^2+x))+((-x^3+2*x^2-x)*log(-1+x)^2+(2*x^4- 
4*x^3+2*x^2)*log(-1+x)-x^5+2*x^4-x^3)*log(x^2)^3),x)
 

Output:

( - 100*e**((2*x)/(log(x - 1)*x - log(x - 1) - x**2 + x)))/(e**((2*x)/(log 
(x - 1)*x - log(x - 1) - x**2 + x))*log(x**2)**2 - 2*e**((log(x - 1)*x**2 
- log(x - 1)*x - x**3 + x**2 + x)/(log(x - 1)*x - log(x - 1) - x**2 + x))* 
log(x**2) + e**(2*x))