\(\int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} (-x^2+(1-x-2 x^3+2 x^4) \log (1-x)+(-1+x) \log (1-x) \log (50 x))}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} (10 x-10 x^2) \log (1-x)+e^{\frac {2 (-x^3+\log (50 x))}{x}} (-x^2+x^3) \log ^2(1-x)} \, dx\) [760]

Optimal result

Integrand size = 139, antiderivative size = 30 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{-5+e^{-x^2+\frac {\log (50 x)}{x}} x \log (1-x)} \] Output:

x/(x*ln(1-x)*exp(ln(50*x)/x-x^2)-5)
 

Mathematica [F(-1)]

Timed out. \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\text {\$Aborted} \] Input:

Integrate[(5 - 5*x + E^((-x^3 + Log[50*x])/x)*(-x^2 + (1 - x - 2*x^3 + 2*x 
^4)*Log[1 - x] + (-1 + x)*Log[1 - x]*Log[50*x]))/(-25 + 25*x + E^((-x^3 + 
Log[50*x])/x)*(10*x - 10*x^2)*Log[1 - x] + E^((2*(-x^3 + Log[50*x]))/x)*(- 
x^2 + x^3)*Log[1 - x]^2),x]
 

Output:

$Aborted
 

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.

\(\displaystyle \int \frac {e^{\frac {\log (50 x)-x^3}{x}} \left (-x^2+\left (2 x^4-2 x^3-x+1\right ) \log (1-x)+(x-1) \log (1-x) \log (50 x)\right )-5 x+5}{\left (x^3-x^2\right ) e^{\frac {2 \left (\log (50 x)-x^3\right )}{x}} \log ^2(1-x)+\left (10 x-10 x^2\right ) e^{\frac {\log (50 x)-x^3}{x}} \log (1-x)+25 x-25} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {e^{2 x^2} \left (-e^{\frac {\log (50 x)-x^3}{x}} \left (-x^2+\left (2 x^4-2 x^3-x+1\right ) \log (1-x)+(x-1) \log (1-x) \log (50 x)\right )+5 x-5\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {50^{\frac {1}{x}} e^{x^2} x^{\frac {1}{x}+1} \log (1-x) \log (50 x)}{(x-1) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )^2}-\frac {50^{\frac {1}{x}} e^{x^2} x^{\frac {1}{x}+1} \log (1-x)}{(x-1) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )^2}-\frac {50^{\frac {1}{x}} e^{x^2} x^{\frac {1}{x}+2}}{(x-1) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )^2}-\frac {2^{\frac {1}{x}+1} 25^{\frac {1}{x}} e^{x^2} x^{\frac {1}{x}+3} \log (1-x)}{(x-1) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )^2}+\frac {2^{\frac {1}{x}+1} 25^{\frac {1}{x}} e^{x^2} x^{\frac {1}{x}+4} \log (1-x)}{(x-1) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )^2}-\frac {5 e^{2 x^2} x}{(x-1) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )^2}+\frac {5 e^{2 x^2}}{(x-1) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )^2}-\frac {50^{\frac {1}{x}} e^{x^2} x^{\frac {1}{x}} \log (1-x) \log (50 x)}{(x-1) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )^2}+\frac {50^{\frac {1}{x}} e^{x^2} x^{\frac {1}{x}} \log (1-x)}{(x-1) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {e^{x^2} \left (50^{\frac {1}{x}} x^{\frac {1}{x}+2}+5 e^{x^2} (x-1)-50^{\frac {1}{x}} (x-1) x^{\frac {1}{x}} \log (1-x) \left (2 x^3+\log (50 x)-1\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {e^{x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)-5 e^{x^2}\right )}+\frac {5 e^{2 x^2} \left (2 x^4 \log (1-x)-2 x^3 \log (1-x)-x^2-x^2 \log (1-x)+x \log (1-x) \log (50 x)+\log (1-x)-\log (1-x) \log (50 x)\right )}{(x-1) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{\frac {1}{x}+1} \log (1-x)\right )^2}\right )dx\)

Input:

Int[(5 - 5*x + E^((-x^3 + Log[50*x])/x)*(-x^2 + (1 - x - 2*x^3 + 2*x^4)*Lo 
g[1 - x] + (-1 + x)*Log[1 - x]*Log[50*x]))/(-25 + 25*x + E^((-x^3 + Log[50 
*x])/x)*(10*x - 10*x^2)*Log[1 - x] + E^((2*(-x^3 + Log[50*x]))/x)*(-x^2 + 
x^3)*Log[1 - x]^2),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 21.30 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93

method	result	size
risch	\(\frac {x}{\ln \left (1-x \right ) \left (50 x \right )^{\frac {1}{x}} {\mathrm e}^{-x^{2}} x -5}\)	\(28\)
parallelrisch	\(\frac {x}{\ln \left (1-x \right ) {\mathrm e}^{\frac {\ln \left (50 x \right )-x^{3}}{x}} x -5}\)	\(30\)

Input:

int((((-1+x)*ln(1-x)*ln(50*x)+(2*x^4-2*x^3-x+1)*ln(1-x)-x^2)*exp((ln(50*x) 
-x^3)/x)-5*x+5)/((x^3-x^2)*ln(1-x)^2*exp((ln(50*x)-x^3)/x)^2+(-10*x^2+10*x 
)*ln(1-x)*exp((ln(50*x)-x^3)/x)+25*x-25),x,method=_RETURNVERBOSE)
 

Output:

x/(ln(1-x)*(50*x)^(1/x)*exp(-x^2)*x-5)
 

Fricas [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{x e^{\left (-\frac {x^{3} - \log \left (50 \, x\right )}{x}\right )} \log \left (-x + 1\right ) - 5} \] Input:

integrate((((-1+x)*log(1-x)*log(50*x)+(2*x^4-2*x^3-x+1)*log(1-x)-x^2)*exp( 
(log(50*x)-x^3)/x)-5*x+5)/((x^3-x^2)*log(1-x)^2*exp((log(50*x)-x^3)/x)^2+( 
-10*x^2+10*x)*log(1-x)*exp((log(50*x)-x^3)/x)+25*x-25),x, algorithm="frica 
s")
 

Output:

x/(x*e^(-(x^3 - log(50*x))/x)*log(-x + 1) - 5)
 

Sympy [A] (verification not implemented)

Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.67 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{x e^{\frac {- x^{3} + \log {\left (50 x \right )}}{x}} \log {\left (1 - x \right )} - 5} \] Input:

integrate((((-1+x)*ln(1-x)*ln(50*x)+(2*x**4-2*x**3-x+1)*ln(1-x)-x**2)*exp( 
(ln(50*x)-x**3)/x)-5*x+5)/((x**3-x**2)*ln(1-x)**2*exp((ln(50*x)-x**3)/x)** 
2+(-10*x**2+10*x)*ln(1-x)*exp((ln(50*x)-x**3)/x)+25*x-25),x)
 

Output:

x/(x*exp((-x**3 + log(50*x))/x)*log(1 - x) - 5)
 

Maxima [A] (verification not implemented)

Time = 0.24 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.47 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x e^{\left (x^{2}\right )}}{x e^{\left (\frac {2 \, \log \left (5\right )}{x} + \frac {\log \left (2\right )}{x} + \frac {\log \left (x\right )}{x}\right )} \log \left (-x + 1\right ) - 5 \, e^{\left (x^{2}\right )}} \] Input:

integrate((((-1+x)*log(1-x)*log(50*x)+(2*x^4-2*x^3-x+1)*log(1-x)-x^2)*exp( 
(log(50*x)-x^3)/x)-5*x+5)/((x^3-x^2)*log(1-x)^2*exp((log(50*x)-x^3)/x)^2+( 
-10*x^2+10*x)*log(1-x)*exp((log(50*x)-x^3)/x)+25*x-25),x, algorithm="maxim 
a")
 

Output:

x*e^(x^2)/(x*e^(2*log(5)/x + log(2)/x + log(x)/x)*log(-x + 1) - 5*e^(x^2))
 

Giac [A] (verification not implemented)

Time = 0.43 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{x e^{\left (-\frac {x^{3} - \log \left (50 \, x\right )}{x}\right )} \log \left (-x + 1\right ) - 5} \] Input:

integrate((((-1+x)*log(1-x)*log(50*x)+(2*x^4-2*x^3-x+1)*log(1-x)-x^2)*exp( 
(log(50*x)-x^3)/x)-5*x+5)/((x^3-x^2)*log(1-x)^2*exp((log(50*x)-x^3)/x)^2+( 
-10*x^2+10*x)*log(1-x)*exp((log(50*x)-x^3)/x)+25*x-25),x, algorithm="giac" 
)
 

Output:

x/(x*e^(-(x^3 - log(50*x))/x)*log(-x + 1) - 5)
 

Mupad [B] (verification not implemented)

Time = 0.86 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.03 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{{50}^{1/x}\,x^{\frac {1}{x}+1}\,{\mathrm {e}}^{-x^2}\,\ln \left (1-x\right )-5} \] Input:

int(-(5*x + exp((log(50*x) - x^3)/x)*(log(1 - x)*(x + 2*x^3 - 2*x^4 - 1) + 
 x^2 - log(50*x)*log(1 - x)*(x - 1)) - 5)/(25*x - exp((2*(log(50*x) - x^3) 
)/x)*log(1 - x)^2*(x^2 - x^3) + exp((log(50*x) - x^3)/x)*log(1 - x)*(10*x 
- 10*x^2) - 25),x)
 

Output:

x/(50^(1/x)*x^(1/x + 1)*exp(-x^2)*log(1 - x) - 5)
 

Reduce [F]

\[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\int \frac {\left (\left (x -1\right ) \mathrm {log}\left (1-x \right ) \mathrm {log}\left (50 x \right )+\left (2 x^{4}-2 x^{3}-x +1\right ) \mathrm {log}\left (1-x \right )-x^{2}\right ) {\mathrm e}^{\frac {\mathrm {log}\left (50 x \right )-x^{3}}{x}}-5 x +5}{\left (x^{3}-x^{2}\right ) \mathrm {log}\left (1-x \right )^{2} \left ({\mathrm e}^{\frac {\mathrm {log}\left (50 x \right )-x^{3}}{x}}\right )^{2}+\left (-10 x^{2}+10 x \right ) \mathrm {log}\left (1-x \right ) {\mathrm e}^{\frac {\mathrm {log}\left (50 x \right )-x^{3}}{x}}+25 x -25}d x \] Input:

int((((-1+x)*log(1-x)*log(50*x)+(2*x^4-2*x^3-x+1)*log(1-x)-x^2)*exp((log(5 
0*x)-x^3)/x)-5*x+5)/((x^3-x^2)*log(1-x)^2*exp((log(50*x)-x^3)/x)^2+(-10*x^ 
2+10*x)*log(1-x)*exp((log(50*x)-x^3)/x)+25*x-25),x)
 

Output:

int((((-1+x)*log(1-x)*log(50*x)+(2*x^4-2*x^3-x+1)*log(1-x)-x^2)*exp((log(5 
0*x)-x^3)/x)-5*x+5)/((x^3-x^2)*log(1-x)^2*exp((log(50*x)-x^3)/x)^2+(-10*x^ 
2+10*x)*log(1-x)*exp((log(50*x)-x^3)/x)+25*x-25),x)