Integrand size = 296, antiderivative size = 32 \[ \int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx=\frac {x}{\log \left (\frac {e^x-5 x}{-e^{e^2}-5 x}+x-\log (x)\right )} \]
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\[ \int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx=\int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (e^{e^2}+5 x\right ) \left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx \\ & = \int \left (\frac {-e^{e^2}+e^{e^2} x+5 \left (1-\frac {e^{e^2}}{5}\right ) x^2-5 x^3-5 \left (1-\frac {e^{e^2}}{5}\right ) x \log (x)+5 x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {5 \left (1-\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )+5 x \log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}\right ) \, dx \\ & = \int \frac {-e^{e^2}+e^{e^2} x+5 \left (1-\frac {e^{e^2}}{5}\right ) x^2-5 x^3-5 \left (1-\frac {e^{e^2}}{5}\right ) x \log (x)+5 x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {5 \left (1-\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )+5 x \log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx \\ & = \int \frac {-5 (-1+x) x^2+e^{e^2} \left (-1+x-x^2\right )+x \left (-5+e^{e^2}+5 x\right ) \log (x)}{\left (e^x-e^{e^2} x-5 x (1+x)+\left (e^{e^2}+5 x\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {-\frac {x \left (-5+e^{e^2}+5 x\right )}{e^{e^2}+5 x}+\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx \\ & = \int \left (\frac {e^{e^2}}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {e^{e^2} \left (1-5 e^{-e^2}\right ) x^2}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {5 x^3}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {5 \left (1-\frac {e^{e^2}}{5}\right ) x \log (x)}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {e^{e^2} x}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {5 x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}\right ) \, dx+\int \left (-\frac {x \left (-5+e^{e^2}+5 x\right )}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {1}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}\right ) \, dx \\ & = 5 \int \frac {x^3}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+5 \int \frac {x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {1}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {x}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (5-e^{e^2}\right ) \int \frac {x \log (x)}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (-5+e^{e^2}\right ) \int \frac {x^2}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx-\int \frac {x \left (-5+e^{e^2}+5 x\right )}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {1}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx \\ & = 5 \int \frac {x^3}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+5 \int \frac {x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {1}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {x}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (5-e^{e^2}\right ) \int \frac {x \log (x)}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (-5+e^{e^2}\right ) \int \frac {x^2}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx-\int \left (-\frac {1}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {x}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}+\frac {e^{e^2}}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}\right ) \, dx+\int \frac {1}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx \\ & = 5 \int \frac {x^3}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+5 \int \frac {x^2 \log (x)}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx-e^{e^2} \int \frac {1}{\left (e^{e^2}+5 x\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {1}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+e^{e^2} \int \frac {x}{\left (e^x-5 \left (1+\frac {e^{e^2}}{5}\right ) x-5 x^2+e^{e^2} \log (x)+5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (5-e^{e^2}\right ) \int \frac {x \log (x)}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\left (-5+e^{e^2}\right ) \int \frac {x^2}{\left (-e^x+5 \left (1+\frac {e^{e^2}}{5}\right ) x+5 x^2-e^{e^2} \log (x)-5 x \log (x)\right ) \log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {1}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx-\int \frac {x}{\log ^2\left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx+\int \frac {1}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx \\ \end{align*}
Time = 0.23 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.53 \[ \int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx=\frac {x}{\log \left (\frac {-e^x+e^{e^2} x+5 x (1+x)-\left (e^{e^2}+5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \]
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Time = 107.28 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.44
method | result | size |
parallelrisch | \(\frac {x}{\ln \left (\frac {\left (-{\mathrm e}^{{\mathrm e}^{2}}-5 x \right ) \ln \left (x \right )+x \,{\mathrm e}^{{\mathrm e}^{2}}-{\mathrm e}^{x}+5 x^{2}+5 x}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right )}\) | \(46\) |
risch | \(\frac {2 i x}{\pi \,\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right ) \operatorname {csgn}\left (i \left (-\left (x -\ln \left (x \right )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \left (x \right )+5\right ) x +{\mathrm e}^{x}\right )\right ) \operatorname {csgn}\left (\frac {i \left (-\left (x -\ln \left (x \right )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \left (x \right )+5\right ) x +{\mathrm e}^{x}\right )}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right )-\pi \,\operatorname {csgn}\left (\frac {i}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right ) {\operatorname {csgn}\left (\frac {i \left (-\left (x -\ln \left (x \right )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \left (x \right )+5\right ) x +{\mathrm e}^{x}\right )}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right )}^{2}+\pi \,\operatorname {csgn}\left (i \left (-\left (x -\ln \left (x \right )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \left (x \right )+5\right ) x +{\mathrm e}^{x}\right )\right ) {\operatorname {csgn}\left (\frac {i \left (-\left (x -\ln \left (x \right )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \left (x \right )+5\right ) x +{\mathrm e}^{x}\right )}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right )}^{2}-\pi {\operatorname {csgn}\left (\frac {i \left (-\left (x -\ln \left (x \right )\right ) {\mathrm e}^{{\mathrm e}^{2}}-5 x^{2}-\left (-5 \ln \left (x \right )+5\right ) x +{\mathrm e}^{x}\right )}{{\mathrm e}^{{\mathrm e}^{2}}+5 x}\right )}^{3}-2 i \ln \left ({\mathrm e}^{{\mathrm e}^{2}}+5 x \right )+2 i \ln \left (\left (x -\ln \left (x \right )\right ) {\mathrm e}^{{\mathrm e}^{2}}+5 x^{2}+\left (-5 \ln \left (x \right )+5\right ) x -{\mathrm e}^{x}\right )}\) | \(321\) |
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Time = 0.26 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.38 \[ \int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx=\frac {x}{\log \left (\frac {5 \, x^{2} + x e^{\left (e^{2}\right )} - {\left (5 \, x + e^{\left (e^{2}\right )}\right )} \log \left (x\right ) + 5 \, x - e^{x}}{5 \, x + e^{\left (e^{2}\right )}}\right )} \]
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Time = 5.19 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.31 \[ \int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx=\frac {x}{\log {\left (\frac {5 x^{2} + 5 x + x e^{e^{2}} + \left (- 5 x - e^{e^{2}}\right ) \log {\left (x \right )} - e^{x}}{5 x + e^{e^{2}}} \right )}} \]
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Time = 0.40 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.38 \[ \int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx=\frac {x}{\log \left (5 \, x^{2} + x {\left (e^{\left (e^{2}\right )} + 5\right )} - {\left (5 \, x + e^{\left (e^{2}\right )}\right )} \log \left (x\right ) - e^{x}\right ) - \log \left (5 \, x + e^{\left (e^{2}\right )}\right )} \]
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Time = 1.38 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.44 \[ \int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx=\frac {x}{\log \left (5 \, x^{2} + x e^{\left (e^{2}\right )} - 5 \, x \log \left (x\right ) - e^{\left (e^{2}\right )} \log \left (x\right ) + 5 \, x - e^{x}\right ) - \log \left (5 \, x + e^{\left (e^{2}\right )}\right )} \]
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Timed out. \[ \int \frac {e^{2 e^2} (-1+x)-25 x^2+25 x^3+e^x \left (5 x-5 x^2\right )+e^{e^2} \left (-5 x-e^x x+10 x^2\right )+\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log \left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )}{\left (-e^{2 e^2} x+5 e^x x-25 x^2-25 x^3+e^{e^2} \left (e^x-5 x-10 x^2\right )+\left (e^{2 e^2}+10 e^{e^2} x+25 x^2\right ) \log (x)\right ) \log ^2\left (\frac {-e^x+5 x+e^{e^2} x+5 x^2+\left (-e^{e^2}-5 x\right ) \log (x)}{e^{e^2}+5 x}\right )} \, dx=-\int -\frac {\ln \left (\frac {5\,x-{\mathrm {e}}^x-\ln \left (x\right )\,\left (5\,x+{\mathrm {e}}^{{\mathrm {e}}^2}\right )+x\,{\mathrm {e}}^{{\mathrm {e}}^2}+5\,x^2}{5\,x+{\mathrm {e}}^{{\mathrm {e}}^2}}\right )\,\left (x\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}-\ln \left (x\right )\,\left (25\,x^2+10\,{\mathrm {e}}^{{\mathrm {e}}^2}\,x+{\mathrm {e}}^{2\,{\mathrm {e}}^2}\right )-5\,x\,{\mathrm {e}}^x+{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (5\,x-{\mathrm {e}}^x+10\,x^2\right )+25\,x^2+25\,x^3\right )+{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (5\,x+x\,{\mathrm {e}}^x-10\,x^2\right )-{\mathrm {e}}^{2\,{\mathrm {e}}^2}\,\left (x-1\right )-{\mathrm {e}}^x\,\left (5\,x-5\,x^2\right )+25\,x^2-25\,x^3}{{\ln \left (\frac {5\,x-{\mathrm {e}}^x-\ln \left (x\right )\,\left (5\,x+{\mathrm {e}}^{{\mathrm {e}}^2}\right )+x\,{\mathrm {e}}^{{\mathrm {e}}^2}+5\,x^2}{5\,x+{\mathrm {e}}^{{\mathrm {e}}^2}}\right )}^2\,\left (x\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}-\ln \left (x\right )\,\left (25\,x^2+10\,{\mathrm {e}}^{{\mathrm {e}}^2}\,x+{\mathrm {e}}^{2\,{\mathrm {e}}^2}\right )-5\,x\,{\mathrm {e}}^x+{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (5\,x-{\mathrm {e}}^x+10\,x^2\right )+25\,x^2+25\,x^3\right )} \,d x \]
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