3.26.43 \(\int \frac {e^{\frac {4+5 x-40 x^2+8 e^x x^2+(13 x^2-e^x x^2) \log (x)-x^2 \log ^2(x)}{-8 x^2+x^2 \log (x)}} (60+35 x-64 x^2-64 e^x x^3+(-8-5 x+16 x^2+16 e^x x^3) \log (x)+(-x^2-e^x x^3) \log ^2(x))}{64 x^3-16 x^3 \log (x)+x^3 \log ^2(x)} \, dx\) [2543]

3.26.43.1 Optimal result

Integrand size = 143, antiderivative size = 34 \[ \int \frac {e^{\frac {4+5 x-40 x^2+8 e^x x^2+\left (13 x^2-e^x x^2\right ) \log (x)-x^2 \log ^2(x)}{-8 x^2+x^2 \log (x)}} \left (60+35 x-64 x^2-64 e^x x^3+\left (-8-5 x+16 x^2+16 e^x x^3\right ) \log (x)+\left (-x^2-e^x x^3\right ) \log ^2(x)\right )}{64 x^3-16 x^3 \log (x)+x^3 \log ^2(x)} \, dx=\frac {e^{5-e^x+\frac {5+\frac {4}{x}}{x-x (9-\log (x))}}}{x} \]

output

exp((5+4/x)/(x-x*(9-ln(x)))-exp(x)-ln(x)+5)
 

3.26.43.2 Mathematica [A] (verified)

Time = 0.45 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.26 \[ \int \frac {e^{\frac {4+5 x-40 x^2+8 e^x x^2+\left (13 x^2-e^x x^2\right ) \log (x)-x^2 \log ^2(x)}{-8 x^2+x^2 \log (x)}} \left (60+35 x-64 x^2-64 e^x x^3+\left (-8-5 x+16 x^2+16 e^x x^3\right ) \log (x)+\left (-x^2-e^x x^3\right ) \log ^2(x)\right )}{64 x^3-16 x^3 \log (x)+x^3 \log ^2(x)} \, dx=\frac {e^{\frac {4+5 x+8 \left (-5+e^x\right ) x^2-\left (-5+e^x\right ) x^2 \log (x)}{x^2 (-8+\log (x))}}}{x} \]

input

Integrate[(E^((4 + 5*x - 40*x^2 + 8*E^x*x^2 + (13*x^2 - E^x*x^2)*Log[x] - 
x^2*Log[x]^2)/(-8*x^2 + x^2*Log[x]))*(60 + 35*x - 64*x^2 - 64*E^x*x^3 + (- 
8 - 5*x + 16*x^2 + 16*E^x*x^3)*Log[x] + (-x^2 - E^x*x^3)*Log[x]^2))/(64*x^ 
3 - 16*x^3*Log[x] + x^3*Log[x]^2),x]
 

output

E^((4 + 5*x + 8*(-5 + E^x)*x^2 - (-5 + E^x)*x^2*Log[x])/(x^2*(-8 + Log[x]) 
))/x
 

3.26.43.3 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.

\(\displaystyle \int \frac {\left (-64 e^x x^3-64 x^2+\left (-e^x x^3-x^2\right ) \log ^2(x)+\left (16 e^x x^3+16 x^2-5 x-8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}\right )}{64 x^3+x^3 \log ^2(x)-16 x^3 \log (x)} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {\left (-64 e^x x^3-64 x^2+\left (-e^x x^3-x^2\right ) \log ^2(x)+\left (16 e^x x^3+16 x^2-5 x-8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}\right )}{x^3 (8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {\log ^2(x) \exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}\right )}{x (\log (x)-8)^2}+\frac {16 \log (x) \exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}\right )}{x (\log (x)-8)^2}-\frac {5 \log (x) \exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}\right )}{x^2 (\log (x)-8)^2}-\exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}+x\right )-\frac {64 \exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}\right )}{x (\log (x)-8)^2}+\frac {35 \exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}\right )}{x^2 (\log (x)-8)^2}-\frac {8 \log (x) \exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}\right )}{x^3 (\log (x)-8)^2}+\frac {60 \exp \left (\frac {8 e^x x^2-40 x^2-x^2 \log ^2(x)+\left (13 x^2-e^x x^2\right ) \log (x)+5 x+4}{x^2 \log (x)-8 x^2}\right )}{x^3 (\log (x)-8)^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \left (-64 e^x x^3-64 x^2-\left (e^x x+1\right ) x^2 \log ^2(x)-\left (-16 e^x x^3-16 x^2+5 x+8\right ) \log (x)+35 x+60\right ) \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(8-\log (x))^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {8 \log (x) x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {60 x^{-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {5 \log (x) x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {35 x^{1-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {\log ^2(x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}+\frac {16 \log (x) x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-\frac {64 x^{2-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}\right )}{(\log (x)-8)^2}-x^{3-\frac {e^x+3 \log (x)-37}{\log (x)-8}} \exp \left (\frac {8 \left (e^x-5\right ) x^2+x^2 \left (-\log ^2(x)\right )+5 x+4}{x^2 (\log (x)-8)}+x\right )\right )dx\)

input

Int[(E^((4 + 5*x - 40*x^2 + 8*E^x*x^2 + (13*x^2 - E^x*x^2)*Log[x] - x^2*Lo 
g[x]^2)/(-8*x^2 + x^2*Log[x]))*(60 + 35*x - 64*x^2 - 64*E^x*x^3 + (-8 - 5* 
x + 16*x^2 + 16*E^x*x^3)*Log[x] + (-x^2 - E^x*x^3)*Log[x]^2))/(64*x^3 - 16 
*x^3*Log[x] + x^3*Log[x]^2),x]
 

output

$Aborted
 

3.26.43.3.1 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] 
]
 

3.26.43.4 Maple [A] (verified)

Time = 18.67 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.56

method	result	size
risch	\({\mathrm e}^{-\frac {x^{2} \ln \left (x \right )^{2}+x^{2} {\mathrm e}^{x} \ln \left (x \right )-13 x^{2} \ln \left (x \right )-8 \,{\mathrm e}^{x} x^{2}+40 x^{2}-5 x -4}{x^{2} \left (\ln \left (x \right )-8\right )}}\)	\(53\)
parallelrisch	\({\mathrm e}^{\frac {-x^{2} \ln \left (x \right )^{2}+\left (-{\mathrm e}^{x} x^{2}+13 x^{2}\right ) \ln \left (x \right )+8 \,{\mathrm e}^{x} x^{2}-40 x^{2}+5 x +4}{x^{2} \left (\ln \left (x \right )-8\right )}}\)	\(54\)

input

int(((-exp(x)*x^3-x^2)*ln(x)^2+(16*exp(x)*x^3+16*x^2-5*x-8)*ln(x)-64*exp(x 
)*x^3-64*x^2+35*x+60)*exp((-x^2*ln(x)^2+(-exp(x)*x^2+13*x^2)*ln(x)+8*exp(x 
)*x^2-40*x^2+5*x+4)/(x^2*ln(x)-8*x^2))/(x^3*ln(x)^2-16*x^3*ln(x)+64*x^3),x 
,method=_RETURNVERBOSE)
 

output

exp(-(x^2*ln(x)^2+x^2*exp(x)*ln(x)-13*x^2*ln(x)-8*exp(x)*x^2+40*x^2-5*x-4) 
/x^2/(ln(x)-8))
 

3.26.43.5 Fricas [A] (verification not implemented)

Time = 0.27 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.68 \[ \int \frac {e^{\frac {4+5 x-40 x^2+8 e^x x^2+\left (13 x^2-e^x x^2\right ) \log (x)-x^2 \log ^2(x)}{-8 x^2+x^2 \log (x)}} \left (60+35 x-64 x^2-64 e^x x^3+\left (-8-5 x+16 x^2+16 e^x x^3\right ) \log (x)+\left (-x^2-e^x x^3\right ) \log ^2(x)\right )}{64 x^3-16 x^3 \log (x)+x^3 \log ^2(x)} \, dx=e^{\left (-\frac {x^{2} \log \left (x\right )^{2} - 8 \, x^{2} e^{x} + 40 \, x^{2} + {\left (x^{2} e^{x} - 13 \, x^{2}\right )} \log \left (x\right ) - 5 \, x - 4}{x^{2} \log \left (x\right ) - 8 \, x^{2}}\right )} \]

input

integrate(((-exp(x)*x^3-x^2)*log(x)^2+(16*exp(x)*x^3+16*x^2-5*x-8)*log(x)- 
64*exp(x)*x^3-64*x^2+35*x+60)*exp((-x^2*log(x)^2+(-exp(x)*x^2+13*x^2)*log( 
x)+8*exp(x)*x^2-40*x^2+5*x+4)/(x^2*log(x)-8*x^2))/(x^3*log(x)^2-16*x^3*log 
(x)+64*x^3),x, algorithm=\
 

output

e^(-(x^2*log(x)^2 - 8*x^2*e^x + 40*x^2 + (x^2*e^x - 13*x^2)*log(x) - 5*x - 
 4)/(x^2*log(x) - 8*x^2))
 

3.26.43.6 Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (20) = 40\).

Time = 0.58 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.59 \[ \int \frac {e^{\frac {4+5 x-40 x^2+8 e^x x^2+\left (13 x^2-e^x x^2\right ) \log (x)-x^2 \log ^2(x)}{-8 x^2+x^2 \log (x)}} \left (60+35 x-64 x^2-64 e^x x^3+\left (-8-5 x+16 x^2+16 e^x x^3\right ) \log (x)+\left (-x^2-e^x x^3\right ) \log ^2(x)\right )}{64 x^3-16 x^3 \log (x)+x^3 \log ^2(x)} \, dx=e^{\frac {8 x^{2} e^{x} - x^{2} \log {\left (x \right )}^{2} - 40 x^{2} + 5 x + \left (- x^{2} e^{x} + 13 x^{2}\right ) \log {\left (x \right )} + 4}{x^{2} \log {\left (x \right )} - 8 x^{2}}} \]

input

integrate(((-exp(x)*x**3-x**2)*ln(x)**2+(16*exp(x)*x**3+16*x**2-5*x-8)*ln( 
x)-64*exp(x)*x**3-64*x**2+35*x+60)*exp((-x**2*ln(x)**2+(-exp(x)*x**2+13*x* 
*2)*ln(x)+8*exp(x)*x**2-40*x**2+5*x+4)/(x**2*ln(x)-8*x**2))/(x**3*ln(x)**2 
-16*x**3*ln(x)+64*x**3),x)
 

output

exp((8*x**2*exp(x) - x**2*log(x)**2 - 40*x**2 + 5*x + (-x**2*exp(x) + 13*x 
**2)*log(x) + 4)/(x**2*log(x) - 8*x**2))
 

3.26.43.7 Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (29) = 58\).

Time = 0.38 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.41 \[ \int \frac {e^{\frac {4+5 x-40 x^2+8 e^x x^2+\left (13 x^2-e^x x^2\right ) \log (x)-x^2 \log ^2(x)}{-8 x^2+x^2 \log (x)}} \left (60+35 x-64 x^2-64 e^x x^3+\left (-8-5 x+16 x^2+16 e^x x^3\right ) \log (x)+\left (-x^2-e^x x^3\right ) \log ^2(x)\right )}{64 x^3-16 x^3 \log (x)+x^3 \log ^2(x)} \, dx=e^{\left (-\frac {e^{x} \log \left (x\right )}{\log \left (x\right ) - 8} - \frac {\log \left (x\right )^{2}}{\log \left (x\right ) - 8} + \frac {8 \, e^{x}}{\log \left (x\right ) - 8} + \frac {13 \, \log \left (x\right )}{\log \left (x\right ) - 8} + \frac {4}{x^{2} \log \left (x\right ) - 8 \, x^{2}} + \frac {5}{x \log \left (x\right ) - 8 \, x} - \frac {40}{\log \left (x\right ) - 8}\right )} \]

input

integrate(((-exp(x)*x^3-x^2)*log(x)^2+(16*exp(x)*x^3+16*x^2-5*x-8)*log(x)- 
64*exp(x)*x^3-64*x^2+35*x+60)*exp((-x^2*log(x)^2+(-exp(x)*x^2+13*x^2)*log( 
x)+8*exp(x)*x^2-40*x^2+5*x+4)/(x^2*log(x)-8*x^2))/(x^3*log(x)^2-16*x^3*log 
(x)+64*x^3),x, algorithm=\
 

output

e^(-e^x*log(x)/(log(x) - 8) - log(x)^2/(log(x) - 8) + 8*e^x/(log(x) - 8) + 
 13*log(x)/(log(x) - 8) + 4/(x^2*log(x) - 8*x^2) + 5/(x*log(x) - 8*x) - 40 
/(log(x) - 8))
 

3.26.43.8 Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 142 vs. \(2 (29) = 58\).

Time = 0.57 (sec) , antiderivative size = 142, normalized size of antiderivative = 4.18 \[ \int \frac {e^{\frac {4+5 x-40 x^2+8 e^x x^2+\left (13 x^2-e^x x^2\right ) \log (x)-x^2 \log ^2(x)}{-8 x^2+x^2 \log (x)}} \left (60+35 x-64 x^2-64 e^x x^3+\left (-8-5 x+16 x^2+16 e^x x^3\right ) \log (x)+\left (-x^2-e^x x^3\right ) \log ^2(x)\right )}{64 x^3-16 x^3 \log (x)+x^3 \log ^2(x)} \, dx=e^{\left (-\frac {x^{2} e^{x} \log \left (x\right )}{x^{2} \log \left (x\right ) - 8 \, x^{2}} - \frac {x^{2} \log \left (x\right )^{2}}{x^{2} \log \left (x\right ) - 8 \, x^{2}} + \frac {8 \, x^{2} e^{x}}{x^{2} \log \left (x\right ) - 8 \, x^{2}} + \frac {13 \, x^{2} \log \left (x\right )}{x^{2} \log \left (x\right ) - 8 \, x^{2}} - \frac {40 \, x^{2}}{x^{2} \log \left (x\right ) - 8 \, x^{2}} + \frac {5 \, x}{x^{2} \log \left (x\right ) - 8 \, x^{2}} + \frac {4}{x^{2} \log \left (x\right ) - 8 \, x^{2}}\right )} \]

input

integrate(((-exp(x)*x^3-x^2)*log(x)^2+(16*exp(x)*x^3+16*x^2-5*x-8)*log(x)- 
64*exp(x)*x^3-64*x^2+35*x+60)*exp((-x^2*log(x)^2+(-exp(x)*x^2+13*x^2)*log( 
x)+8*exp(x)*x^2-40*x^2+5*x+4)/(x^2*log(x)-8*x^2))/(x^3*log(x)^2-16*x^3*log 
(x)+64*x^3),x, algorithm=\
 

output

e^(-x^2*e^x*log(x)/(x^2*log(x) - 8*x^2) - x^2*log(x)^2/(x^2*log(x) - 8*x^2 
) + 8*x^2*e^x/(x^2*log(x) - 8*x^2) + 13*x^2*log(x)/(x^2*log(x) - 8*x^2) - 
40*x^2/(x^2*log(x) - 8*x^2) + 5*x/(x^2*log(x) - 8*x^2) + 4/(x^2*log(x) - 8 
*x^2))
 

3.26.43.9 Mupad [B] (verification not implemented)

Time = 13.74 (sec) , antiderivative size = 117, normalized size of antiderivative = 3.44 \[ \int \frac {e^{\frac {4+5 x-40 x^2+8 e^x x^2+\left (13 x^2-e^x x^2\right ) \log (x)-x^2 \log ^2(x)}{-8 x^2+x^2 \log (x)}} \left (60+35 x-64 x^2-64 e^x x^3+\left (-8-5 x+16 x^2+16 e^x x^3\right ) \log (x)+\left (-x^2-e^x x^3\right ) \log ^2(x)\right )}{64 x^3-16 x^3 \log (x)+x^3 \log ^2(x)} \, dx=\frac {{\mathrm {e}}^{\frac {5\,x}{x^2\,\ln \left (x\right )-8\,x^2}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^x}{x^2\,\ln \left (x\right )-8\,x^2}}\,{\mathrm {e}}^{-\frac {40\,x^2}{x^2\,\ln \left (x\right )-8\,x^2}}\,{\mathrm {e}}^{\frac {4}{x^2\,\ln \left (x\right )-8\,x^2}}\,{\mathrm {e}}^{-\frac {x^2\,{\ln \left (x\right )}^2}{x^2\,\ln \left (x\right )-8\,x^2}}}{x^{\frac {{\mathrm {e}}^x-13}{\ln \left (x\right )-8}}} \]

input

int(-(exp((5*x + 8*x^2*exp(x) - x^2*log(x)^2 - 40*x^2 - log(x)*(x^2*exp(x) 
 - 13*x^2) + 4)/(x^2*log(x) - 8*x^2))*(64*x^3*exp(x) - 35*x + log(x)*(5*x 
- 16*x^3*exp(x) - 16*x^2 + 8) + 64*x^2 + log(x)^2*(x^3*exp(x) + x^2) - 60) 
)/(x^3*log(x)^2 - 16*x^3*log(x) + 64*x^3),x)
 

output

(exp((5*x)/(x^2*log(x) - 8*x^2))*exp((8*x^2*exp(x))/(x^2*log(x) - 8*x^2))* 
exp(-(40*x^2)/(x^2*log(x) - 8*x^2))*exp(4/(x^2*log(x) - 8*x^2))*exp(-(x^2* 
log(x)^2)/(x^2*log(x) - 8*x^2)))/x^((exp(x) - 13)/(log(x) - 8))