3.1.82 \(\int \frac {e^{\frac {e^x (-1+x)+x-x^2-x \log (\frac {x^2}{3})+x \log (1-x^2)}{\log (\frac {x^2}{3})-\log (1-x^2)}} (2 e^x-2 x+(-1-2 x-x^2) \log ^2(\frac {x^2}{3})+(-x+x^2+2 x^3+e^x (-x^2-x^3)) \log (1-x^2)+(-1-2 x-x^2) \log ^2(1-x^2)+\log (\frac {x^2}{3}) (x-x^2-2 x^3+e^x (x^2+x^3)+(2+4 x+2 x^2) \log (1-x^2)))}{(x^2+x^3) \log ^2(\frac {x^2}{3})+(-2 x^2-2 x^3) \log (\frac {x^2}{3}) \log (1-x^2)+(x^2+x^3) \log ^2(1-x^2)} \, dx\) [82]

3.1.82.1 Optimal result

Integrand size = 265, antiderivative size = 44 \[ \int \frac {e^{\frac {e^x (-1+x)+x-x^2-x \log \left (\frac {x^2}{3}\right )+x \log \left (1-x^2\right )}{\log \left (\frac {x^2}{3}\right )-\log \left (1-x^2\right )}} \left (2 e^x-2 x+\left (-1-2 x-x^2\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-x+x^2+2 x^3+e^x \left (-x^2-x^3\right )\right ) \log \left (1-x^2\right )+\left (-1-2 x-x^2\right ) \log ^2\left (1-x^2\right )+\log \left (\frac {x^2}{3}\right ) \left (x-x^2-2 x^3+e^x \left (x^2+x^3\right )+\left (2+4 x+2 x^2\right ) \log \left (1-x^2\right )\right )\right )}{\left (x^2+x^3\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-2 x^2-2 x^3\right ) \log \left (\frac {x^2}{3}\right ) \log \left (1-x^2\right )+\left (x^2+x^3\right ) \log ^2\left (1-x^2\right )} \, dx=\frac {e^{-x+\frac {(1-x) \left (-e^x+x\right )}{\log \left (\frac {x^2}{3}\right )-\log \left (1-x^2\right )}}}{x} \]

output

exp((1-x)/(ln(1/3*x^2)-ln(-x^2+1))*(x-exp(x))-x)/x
 

3.1.82.2 Mathematica [F]

\[ \int \frac {e^{\frac {e^x (-1+x)+x-x^2-x \log \left (\frac {x^2}{3}\right )+x \log \left (1-x^2\right )}{\log \left (\frac {x^2}{3}\right )-\log \left (1-x^2\right )}} \left (2 e^x-2 x+\left (-1-2 x-x^2\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-x+x^2+2 x^3+e^x \left (-x^2-x^3\right )\right ) \log \left (1-x^2\right )+\left (-1-2 x-x^2\right ) \log ^2\left (1-x^2\right )+\log \left (\frac {x^2}{3}\right ) \left (x-x^2-2 x^3+e^x \left (x^2+x^3\right )+\left (2+4 x+2 x^2\right ) \log \left (1-x^2\right )\right )\right )}{\left (x^2+x^3\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-2 x^2-2 x^3\right ) \log \left (\frac {x^2}{3}\right ) \log \left (1-x^2\right )+\left (x^2+x^3\right ) \log ^2\left (1-x^2\right )} \, dx=\int \frac {e^{\frac {e^x (-1+x)+x-x^2-x \log \left (\frac {x^2}{3}\right )+x \log \left (1-x^2\right )}{\log \left (\frac {x^2}{3}\right )-\log \left (1-x^2\right )}} \left (2 e^x-2 x+\left (-1-2 x-x^2\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-x+x^2+2 x^3+e^x \left (-x^2-x^3\right )\right ) \log \left (1-x^2\right )+\left (-1-2 x-x^2\right ) \log ^2\left (1-x^2\right )+\log \left (\frac {x^2}{3}\right ) \left (x-x^2-2 x^3+e^x \left (x^2+x^3\right )+\left (2+4 x+2 x^2\right ) \log \left (1-x^2\right )\right )\right )}{\left (x^2+x^3\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-2 x^2-2 x^3\right ) \log \left (\frac {x^2}{3}\right ) \log \left (1-x^2\right )+\left (x^2+x^3\right ) \log ^2\left (1-x^2\right )} \, dx \]

input

Integrate[(E^((E^x*(-1 + x) + x - x^2 - x*Log[x^2/3] + x*Log[1 - x^2])/(Lo 
g[x^2/3] - Log[1 - x^2]))*(2*E^x - 2*x + (-1 - 2*x - x^2)*Log[x^2/3]^2 + ( 
-x + x^2 + 2*x^3 + E^x*(-x^2 - x^3))*Log[1 - x^2] + (-1 - 2*x - x^2)*Log[1 
 - x^2]^2 + Log[x^2/3]*(x - x^2 - 2*x^3 + E^x*(x^2 + x^3) + (2 + 4*x + 2*x 
^2)*Log[1 - x^2])))/((x^2 + x^3)*Log[x^2/3]^2 + (-2*x^2 - 2*x^3)*Log[x^2/3 
]*Log[1 - x^2] + (x^2 + x^3)*Log[1 - x^2]^2),x]
 

output

Integrate[(E^((E^x*(-1 + x) + x - x^2 - x*Log[x^2/3] + x*Log[1 - x^2])/(Lo 
g[x^2/3] - Log[1 - x^2]))*(2*E^x - 2*x + (-1 - 2*x - x^2)*Log[x^2/3]^2 + ( 
-x + x^2 + 2*x^3 + E^x*(-x^2 - x^3))*Log[1 - x^2] + (-1 - 2*x - x^2)*Log[1 
 - x^2]^2 + Log[x^2/3]*(x - x^2 - 2*x^3 + E^x*(x^2 + x^3) + (2 + 4*x + 2*x 
^2)*Log[1 - x^2])))/((x^2 + x^3)*Log[x^2/3]^2 + (-2*x^2 - 2*x^3)*Log[x^2/3 
]*Log[1 - x^2] + (x^2 + x^3)*Log[1 - x^2]^2), x]
 

3.1.82.3 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.

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

\(\Big \downarrow \) 7292

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 7239

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

\(\Big \downarrow \) 7293

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

input

Int[(E^((E^x*(-1 + x) + x - x^2 - x*Log[x^2/3] + x*Log[1 - x^2])/(Log[x^2/ 
3] - Log[1 - x^2]))*(2*E^x - 2*x + (-1 - 2*x - x^2)*Log[x^2/3]^2 + (-x + x 
^2 + 2*x^3 + E^x*(-x^2 - x^3))*Log[1 - x^2] + (-1 - 2*x - x^2)*Log[1 - x^2 
]^2 + Log[x^2/3]*(x - x^2 - 2*x^3 + E^x*(x^2 + x^3) + (2 + 4*x + 2*x^2)*Lo 
g[1 - x^2])))/((x^2 + x^3)*Log[x^2/3]^2 + (-2*x^2 - 2*x^3)*Log[x^2/3]*Log[ 
1 - x^2] + (x^2 + x^3)*Log[1 - x^2]^2),x]
 

output

$Aborted
 

3.1.82.3.1 Defintions of rubi rules used

rule 7239

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

rule 7292

Int[u_, x_Symbol] :> With[{v = NormalizeIntegrand[u, x]}, Int[v, x] /; v =! 
= u]
 

rule 7293

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v] 
]
 

3.1.82.4 Maple [C] (warning: unable to verify)

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

Time = 0.30 (sec) , antiderivative size = 169, normalized size of antiderivative = 3.84

\[\frac {{\mathrm e}^{-\frac {i \pi x \operatorname {csgn}\left (i x^{2}\right )^{3}-2 i \pi x \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+i \pi x \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+2 x \ln \left (3\right )-4 x \ln \left (x \right )+2 x \ln \left (-x^{2}+1\right )+2 \,{\mathrm e}^{x} x -2 x^{2}-2 \,{\mathrm e}^{x}+2 x}{i \pi \operatorname {csgn}\left (i x^{2}\right )^{3}-2 i \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+i \pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+2 \ln \left (3\right )-4 \ln \left (x \right )+2 \ln \left (-x^{2}+1\right )}}}{x}\]

input

int(((-x^2-2*x-1)*ln(1/3*x^2)^2+((2*x^2+4*x+2)*ln(-x^2+1)+(x^3+x^2)*exp(x) 
-2*x^3-x^2+x)*ln(1/3*x^2)+(-x^2-2*x-1)*ln(-x^2+1)^2+((-x^3-x^2)*exp(x)+2*x 
^3+x^2-x)*ln(-x^2+1)+2*exp(x)-2*x)*exp((-x*ln(1/3*x^2)+x*ln(-x^2+1)+(-1+x) 
*exp(x)-x^2+x)/(ln(1/3*x^2)-ln(-x^2+1)))/((x^3+x^2)*ln(1/3*x^2)^2+(-2*x^3- 
2*x^2)*ln(-x^2+1)*ln(1/3*x^2)+(x^3+x^2)*ln(-x^2+1)^2),x)
 

output

1/x*exp(-(I*x*Pi*csgn(I*x^2)^3-2*I*x*Pi*csgn(I*x^2)^2*csgn(I*x)+I*x*Pi*csg 
n(I*x^2)*csgn(I*x)^2+2*x*ln(3)-4*x*ln(x)+2*x*ln(-x^2+1)+2*exp(x)*x-2*x^2-2 
*exp(x)+2*x)/(I*Pi*csgn(I*x^2)^3-2*I*Pi*csgn(I*x^2)^2*csgn(I*x)+I*Pi*csgn( 
I*x^2)*csgn(I*x)^2+2*ln(3)-4*ln(x)+2*ln(-x^2+1)))
 

3.1.82.5 Fricas [A] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.34 \[ \int \frac {e^{\frac {e^x (-1+x)+x-x^2-x \log \left (\frac {x^2}{3}\right )+x \log \left (1-x^2\right )}{\log \left (\frac {x^2}{3}\right )-\log \left (1-x^2\right )}} \left (2 e^x-2 x+\left (-1-2 x-x^2\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-x+x^2+2 x^3+e^x \left (-x^2-x^3\right )\right ) \log \left (1-x^2\right )+\left (-1-2 x-x^2\right ) \log ^2\left (1-x^2\right )+\log \left (\frac {x^2}{3}\right ) \left (x-x^2-2 x^3+e^x \left (x^2+x^3\right )+\left (2+4 x+2 x^2\right ) \log \left (1-x^2\right )\right )\right )}{\left (x^2+x^3\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-2 x^2-2 x^3\right ) \log \left (\frac {x^2}{3}\right ) \log \left (1-x^2\right )+\left (x^2+x^3\right ) \log ^2\left (1-x^2\right )} \, dx=\frac {e^{\left (-\frac {x^{2} - {\left (x - 1\right )} e^{x} + x \log \left (\frac {1}{3} \, x^{2}\right ) - x \log \left (-x^{2} + 1\right ) - x}{\log \left (\frac {1}{3} \, x^{2}\right ) - \log \left (-x^{2} + 1\right )}\right )}}{x} \]

input

integrate(((-x^2-2*x-1)*log(1/3*x^2)^2+((2*x^2+4*x+2)*log(-x^2+1)+(x^3+x^2 
)*exp(x)-2*x^3-x^2+x)*log(1/3*x^2)+(-x^2-2*x-1)*log(-x^2+1)^2+((-x^3-x^2)* 
exp(x)+2*x^3+x^2-x)*log(-x^2+1)+2*exp(x)-2*x)*exp((-x*log(1/3*x^2)+x*log(- 
x^2+1)+(-1+x)*exp(x)-x^2+x)/(log(1/3*x^2)-log(-x^2+1)))/((x^3+x^2)*log(1/3 
*x^2)^2+(-2*x^3-2*x^2)*log(-x^2+1)*log(1/3*x^2)+(x^3+x^2)*log(-x^2+1)^2),x 
, algorithm=\
 

output

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

3.1.82.6 Sympy [A] (verification not implemented)

Time = 8.12 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {e^x (-1+x)+x-x^2-x \log \left (\frac {x^2}{3}\right )+x \log \left (1-x^2\right )}{\log \left (\frac {x^2}{3}\right )-\log \left (1-x^2\right )}} \left (2 e^x-2 x+\left (-1-2 x-x^2\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-x+x^2+2 x^3+e^x \left (-x^2-x^3\right )\right ) \log \left (1-x^2\right )+\left (-1-2 x-x^2\right ) \log ^2\left (1-x^2\right )+\log \left (\frac {x^2}{3}\right ) \left (x-x^2-2 x^3+e^x \left (x^2+x^3\right )+\left (2+4 x+2 x^2\right ) \log \left (1-x^2\right )\right )\right )}{\left (x^2+x^3\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-2 x^2-2 x^3\right ) \log \left (\frac {x^2}{3}\right ) \log \left (1-x^2\right )+\left (x^2+x^3\right ) \log ^2\left (1-x^2\right )} \, dx=\frac {e^{\frac {- x^{2} - x \log {\left (\frac {x^{2}}{3} \right )} + x \log {\left (1 - x^{2} \right )} + x + \left (x - 1\right ) e^{x}}{\log {\left (\frac {x^{2}}{3} \right )} - \log {\left (1 - x^{2} \right )}}}}{x} \]

input

integrate(((-x**2-2*x-1)*ln(1/3*x**2)**2+((2*x**2+4*x+2)*ln(-x**2+1)+(x**3 
+x**2)*exp(x)-2*x**3-x**2+x)*ln(1/3*x**2)+(-x**2-2*x-1)*ln(-x**2+1)**2+((- 
x**3-x**2)*exp(x)+2*x**3+x**2-x)*ln(-x**2+1)+2*exp(x)-2*x)*exp((-x*ln(1/3* 
x**2)+x*ln(-x**2+1)+(-1+x)*exp(x)-x**2+x)/(ln(1/3*x**2)-ln(-x**2+1)))/((x* 
*3+x**2)*ln(1/3*x**2)**2+(-2*x**3-2*x**2)*ln(-x**2+1)*ln(1/3*x**2)+(x**3+x 
**2)*ln(-x**2+1)**2),x)
 

output

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

3.1.82.7 Maxima [F]

\[ \int \frac {e^{\frac {e^x (-1+x)+x-x^2-x \log \left (\frac {x^2}{3}\right )+x \log \left (1-x^2\right )}{\log \left (\frac {x^2}{3}\right )-\log \left (1-x^2\right )}} \left (2 e^x-2 x+\left (-1-2 x-x^2\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-x+x^2+2 x^3+e^x \left (-x^2-x^3\right )\right ) \log \left (1-x^2\right )+\left (-1-2 x-x^2\right ) \log ^2\left (1-x^2\right )+\log \left (\frac {x^2}{3}\right ) \left (x-x^2-2 x^3+e^x \left (x^2+x^3\right )+\left (2+4 x+2 x^2\right ) \log \left (1-x^2\right )\right )\right )}{\left (x^2+x^3\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-2 x^2-2 x^3\right ) \log \left (\frac {x^2}{3}\right ) \log \left (1-x^2\right )+\left (x^2+x^3\right ) \log ^2\left (1-x^2\right )} \, dx=\int { -\frac {{\left ({\left (x^{2} + 2 \, x + 1\right )} \log \left (\frac {1}{3} \, x^{2}\right )^{2} + {\left (x^{2} + 2 \, x + 1\right )} \log \left (-x^{2} + 1\right )^{2} + {\left (2 \, x^{3} + x^{2} - {\left (x^{3} + x^{2}\right )} e^{x} - 2 \, {\left (x^{2} + 2 \, x + 1\right )} \log \left (-x^{2} + 1\right ) - x\right )} \log \left (\frac {1}{3} \, x^{2}\right ) - {\left (2 \, x^{3} + x^{2} - {\left (x^{3} + x^{2}\right )} e^{x} - x\right )} \log \left (-x^{2} + 1\right ) + 2 \, x - 2 \, e^{x}\right )} e^{\left (-\frac {x^{2} - {\left (x - 1\right )} e^{x} + x \log \left (\frac {1}{3} \, x^{2}\right ) - x \log \left (-x^{2} + 1\right ) - x}{\log \left (\frac {1}{3} \, x^{2}\right ) - \log \left (-x^{2} + 1\right )}\right )}}{{\left (x^{3} + x^{2}\right )} \log \left (\frac {1}{3} \, x^{2}\right )^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \left (\frac {1}{3} \, x^{2}\right ) \log \left (-x^{2} + 1\right ) + {\left (x^{3} + x^{2}\right )} \log \left (-x^{2} + 1\right )^{2}} \,d x } \]

input

integrate(((-x^2-2*x-1)*log(1/3*x^2)^2+((2*x^2+4*x+2)*log(-x^2+1)+(x^3+x^2 
)*exp(x)-2*x^3-x^2+x)*log(1/3*x^2)+(-x^2-2*x-1)*log(-x^2+1)^2+((-x^3-x^2)* 
exp(x)+2*x^3+x^2-x)*log(-x^2+1)+2*exp(x)-2*x)*exp((-x*log(1/3*x^2)+x*log(- 
x^2+1)+(-1+x)*exp(x)-x^2+x)/(log(1/3*x^2)-log(-x^2+1)))/((x^3+x^2)*log(1/3 
*x^2)^2+(-2*x^3-2*x^2)*log(-x^2+1)*log(1/3*x^2)+(x^3+x^2)*log(-x^2+1)^2),x 
, algorithm=\
 

output

-integrate(((x^2 + 2*x + 1)*log(1/3*x^2)^2 + (x^2 + 2*x + 1)*log(-x^2 + 1) 
^2 + (2*x^3 + x^2 - (x^3 + x^2)*e^x - 2*(x^2 + 2*x + 1)*log(-x^2 + 1) - x) 
*log(1/3*x^2) - (2*x^3 + x^2 - (x^3 + x^2)*e^x - x)*log(-x^2 + 1) + 2*x - 
2*e^x)*e^(-(x^2 - (x - 1)*e^x + x*log(1/3*x^2) - x*log(-x^2 + 1) - x)/(log 
(1/3*x^2) - log(-x^2 + 1)))/((x^3 + x^2)*log(1/3*x^2)^2 - 2*(x^3 + x^2)*lo 
g(1/3*x^2)*log(-x^2 + 1) + (x^3 + x^2)*log(-x^2 + 1)^2), x)
 

3.1.82.8 Giac [A] (verification not implemented)

Time = 4.08 (sec) , antiderivative size = 43, normalized size of antiderivative = 0.98 \[ \int \frac {e^{\frac {e^x (-1+x)+x-x^2-x \log \left (\frac {x^2}{3}\right )+x \log \left (1-x^2\right )}{\log \left (\frac {x^2}{3}\right )-\log \left (1-x^2\right )}} \left (2 e^x-2 x+\left (-1-2 x-x^2\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-x+x^2+2 x^3+e^x \left (-x^2-x^3\right )\right ) \log \left (1-x^2\right )+\left (-1-2 x-x^2\right ) \log ^2\left (1-x^2\right )+\log \left (\frac {x^2}{3}\right ) \left (x-x^2-2 x^3+e^x \left (x^2+x^3\right )+\left (2+4 x+2 x^2\right ) \log \left (1-x^2\right )\right )\right )}{\left (x^2+x^3\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-2 x^2-2 x^3\right ) \log \left (\frac {x^2}{3}\right ) \log \left (1-x^2\right )+\left (x^2+x^3\right ) \log ^2\left (1-x^2\right )} \, dx=\frac {e^{\left (-x + \frac {x^{2} - x e^{x} - x + e^{x}}{\log \left (3\right ) - \log \left (x^{2}\right ) + \log \left (-x^{2} + 1\right )}\right )}}{x} \]

input

integrate(((-x^2-2*x-1)*log(1/3*x^2)^2+((2*x^2+4*x+2)*log(-x^2+1)+(x^3+x^2 
)*exp(x)-2*x^3-x^2+x)*log(1/3*x^2)+(-x^2-2*x-1)*log(-x^2+1)^2+((-x^3-x^2)* 
exp(x)+2*x^3+x^2-x)*log(-x^2+1)+2*exp(x)-2*x)*exp((-x*log(1/3*x^2)+x*log(- 
x^2+1)+(-1+x)*exp(x)-x^2+x)/(log(1/3*x^2)-log(-x^2+1)))/((x^3+x^2)*log(1/3 
*x^2)^2+(-2*x^3-2*x^2)*log(-x^2+1)*log(1/3*x^2)+(x^3+x^2)*log(-x^2+1)^2),x 
, algorithm=\
 

output

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

3.1.82.9 Mupad [B] (verification not implemented)

Time = 9.11 (sec) , antiderivative size = 157, normalized size of antiderivative = 3.57 \[ \int \frac {e^{\frac {e^x (-1+x)+x-x^2-x \log \left (\frac {x^2}{3}\right )+x \log \left (1-x^2\right )}{\log \left (\frac {x^2}{3}\right )-\log \left (1-x^2\right )}} \left (2 e^x-2 x+\left (-1-2 x-x^2\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-x+x^2+2 x^3+e^x \left (-x^2-x^3\right )\right ) \log \left (1-x^2\right )+\left (-1-2 x-x^2\right ) \log ^2\left (1-x^2\right )+\log \left (\frac {x^2}{3}\right ) \left (x-x^2-2 x^3+e^x \left (x^2+x^3\right )+\left (2+4 x+2 x^2\right ) \log \left (1-x^2\right )\right )\right )}{\left (x^2+x^3\right ) \log ^2\left (\frac {x^2}{3}\right )+\left (-2 x^2-2 x^3\right ) \log \left (\frac {x^2}{3}\right ) \log \left (1-x^2\right )+\left (x^2+x^3\right ) \log ^2\left (1-x^2\right )} \, dx=\frac {{\mathrm {e}}^{-\frac {x}{\ln \left (1-x^2\right )-\ln \left (x^2\right )+\ln \left (3\right )}}\,{\mathrm {e}}^{\frac {x^2}{\ln \left (1-x^2\right )-\ln \left (x^2\right )+\ln \left (3\right )}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{\ln \left (1-x^2\right )-\ln \left (x^2\right )+\ln \left (3\right )}}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^x}{\ln \left (1-x^2\right )-\ln \left (x^2\right )+\ln \left (3\right )}}\,{\left (\frac {x^2}{3}\right )}^{\frac {x}{\ln \left (1-x^2\right )-\ln \left (x^2\right )+\ln \left (3\right )}}}{x\,{\left (1-x^2\right )}^{\frac {x}{\ln \left (1-x^2\right )-\ln \left (x^2\right )+\ln \left (3\right )}}} \]

input

int(-(exp(-(x + exp(x)*(x - 1) - x*log(x^2/3) - x^2 + x*log(1 - x^2))/(log 
(1 - x^2) - log(x^2/3)))*(2*x - 2*exp(x) - log(x^2/3)*(x + exp(x)*(x^2 + x 
^3) + log(1 - x^2)*(4*x + 2*x^2 + 2) - x^2 - 2*x^3) + log(x^2/3)^2*(2*x + 
x^2 + 1) + log(1 - x^2)^2*(2*x + x^2 + 1) + log(1 - x^2)*(x + exp(x)*(x^2 
+ x^3) - x^2 - 2*x^3)))/(log(x^2/3)^2*(x^2 + x^3) + log(1 - x^2)^2*(x^2 + 
x^3) - log(1 - x^2)*log(x^2/3)*(2*x^2 + 2*x^3)),x)
 

output

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