Integrand size = 139, antiderivative size = 30 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{-5+e^{-x^2+\frac {\log (50 x)}{x}} x \log (1-x)} \]
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\[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{x^2} \left (5 e^{x^2} (-1+x)+50^{\frac {1}{x}} x^{2+\frac {1}{x}}-50^{\frac {1}{x}} (-1+x) x^{\frac {1}{x}} \log (1-x) \left (-1+2 x^3+\log (50 x)\right )\right )}{(1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2} \, dx \\ & = \int \left (\frac {e^{x^2} \left (-x^2+\log (1-x)-x \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{(-1+x) x \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}+\frac {5 e^{2 x^2} \left (-x^2+\log (1-x)-x^2 \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{(-1+x) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}\right ) \, dx \\ & = 5 \int \frac {e^{2 x^2} \left (-x^2+\log (1-x)-x^2 \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{(-1+x) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2} \, dx+\int \frac {e^{x^2} \left (-x^2+\log (1-x)-x \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{(-1+x) x \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )} \, dx \\ & = 5 \int \frac {e^{2 x^2} \left (x^2-(-1+x) \log (1-x) \left (-1-x+2 x^3+\log (50 x)\right )\right )}{(1-x) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2} \, dx+\int \frac {e^{x^2} \left (-x^2+(-1+x) \log (1-x) \left (-1+2 x^3+\log (50 x)\right )\right )}{(1-x) x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )} \, dx \\ & = 5 \int \left (\frac {e^{2 x^2} \left (-x^2+\log (1-x)-x^2 \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{(-1+x) \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}-\frac {e^{2 x^2} \left (-x^2+\log (1-x)-x^2 \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{x \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}\right ) \, dx+\int \left (\frac {e^{x^2} \left (-x^2+\log (1-x)-x \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{(-1+x) \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}-\frac {e^{x^2} \left (-x^2+\log (1-x)-x \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{x \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}\right ) \, dx \\ & = 5 \int \frac {e^{2 x^2} \left (-x^2+\log (1-x)-x^2 \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{(-1+x) \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2} \, dx-5 \int \frac {e^{2 x^2} \left (-x^2+\log (1-x)-x^2 \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{x \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2} \, dx+\int \frac {e^{x^2} \left (-x^2+\log (1-x)-x \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{(-1+x) \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )} \, dx-\int \frac {e^{x^2} \left (-x^2+\log (1-x)-x \log (1-x)-2 x^3 \log (1-x)+2 x^4 \log (1-x)-\log (1-x) \log (50 x)+x \log (1-x) \log (50 x)\right )}{x \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )} \, dx \\ & = 5 \int \frac {e^{2 x^2} \left (x^2-(-1+x) \log (1-x) \left (-1-x+2 x^3+\log (50 x)\right )\right )}{(1-x) \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2} \, dx-5 \int \frac {e^{2 x^2} \left (-x^2+(-1+x) \log (1-x) \left (-1-x+2 x^3+\log (50 x)\right )\right )}{x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2} \, dx-\int \frac {e^{x^2} \left (x^2-(-1+x) \log (1-x) \left (-1+2 x^3+\log (50 x)\right )\right )}{x \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )} \, dx+\int \frac {e^{x^2} \left (-x^2+(-1+x) \log (1-x) \left (-1+2 x^3+\log (50 x)\right )\right )}{(1-x) \log (1-x) \left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )} \, dx \\ & = -\left (5 \int \left (\frac {e^{2 x^2}}{x \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}-\frac {e^{2 x^2} x}{\left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}-\frac {2 e^{2 x^2} x^2}{\left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}+\frac {2 e^{2 x^2} x^3}{\left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}-\frac {e^{2 x^2} x}{\log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}+\frac {e^{2 x^2} \log (50 x)}{\left (5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}-\frac {e^{2 x^2} \log (50 x)}{x \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}\right ) \, dx\right )+5 \int \left (\frac {e^{2 x^2}}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}-\frac {e^{2 x^2} x^2}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}-\frac {2 e^{2 x^2} x^3}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}+\frac {2 e^{2 x^2} x^4}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}-\frac {e^{2 x^2} x^2}{(-1+x) \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}-\frac {e^{2 x^2} \log (50 x)}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}+\frac {e^{2 x^2} x \log (50 x)}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )^2}\right ) \, dx-\int \left (\frac {e^{x^2}}{5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)}+\frac {e^{x^2}}{x \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}-\frac {2 e^{x^2} x^2}{-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)}+\frac {2 e^{x^2} x^3}{-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)}-\frac {e^{x^2} x}{\log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}-\frac {e^{x^2} \log (50 x)}{5 e^{x^2}-50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)}-\frac {e^{x^2} \log (50 x)}{x \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}\right ) \, dx+\int \left (\frac {e^{x^2}}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}-\frac {e^{x^2} x}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}-\frac {2 e^{x^2} x^3}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}+\frac {2 e^{x^2} x^4}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}-\frac {e^{x^2} x^2}{(-1+x) \log (1-x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}-\frac {e^{x^2} \log (50 x)}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}+\frac {e^{x^2} x \log (50 x)}{(-1+x) \left (-5 e^{x^2}+50^{\frac {1}{x}} x^{1+\frac {1}{x}} \log (1-x)\right )}\right ) \, dx \\ & = \text {Too large to display} \\ \end{align*}
Timed out. \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\text {\$Aborted} \]
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Time = 16.31 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93
method | result | size |
risch | \(\frac {x}{\left (50 x \right )^{\frac {1}{x}} {\mathrm e}^{-x^{2}} \ln \left (1-x \right ) x -5}\) | \(28\) |
parallelrisch | \(\frac {x}{\ln \left (1-x \right ) {\mathrm e}^{\frac {\ln \left (50 x \right )-x^{3}}{x}} x -5}\) | \(30\) |
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Time = 0.25 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{x e^{\left (-\frac {x^{3} - \log \left (50 \, x\right )}{x}\right )} \log \left (-x + 1\right ) - 5} \]
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Time = 0.22 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.67 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{x e^{\frac {- x^{3} + \log {\left (50 x \right )}}{x}} \log {\left (1 - x \right )} - 5} \]
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Time = 0.36 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.47 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x e^{\left (x^{2}\right )}}{x e^{\left (\frac {2 \, \log \left (5\right )}{x} + \frac {\log \left (2\right )}{x} + \frac {\log \left (x\right )}{x}\right )} \log \left (-x + 1\right ) - 5 \, e^{\left (x^{2}\right )}} \]
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Time = 0.65 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{x e^{\left (-\frac {x^{3} - \log \left (50 \, x\right )}{x}\right )} \log \left (-x + 1\right ) - 5} \]
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Time = 8.46 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.03 \[ \int \frac {5-5 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (-x^2+\left (1-x-2 x^3+2 x^4\right ) \log (1-x)+(-1+x) \log (1-x) \log (50 x)\right )}{-25+25 x+e^{\frac {-x^3+\log (50 x)}{x}} \left (10 x-10 x^2\right ) \log (1-x)+e^{\frac {2 \left (-x^3+\log (50 x)\right )}{x}} \left (-x^2+x^3\right ) \log ^2(1-x)} \, dx=\frac {x}{{50}^{1/x}\,x^{\frac {1}{x}+1}\,{\mathrm {e}}^{-x^2}\,\ln \left (1-x\right )-5} \]
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