Integrand size = 272, antiderivative size = 26 \[ \int \frac {-5 x+5 e^x x+\left (-2+e^x (5-5 x)-3 x+5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (\left (2+3 x-5 x^2+e^x (-5+5 x)\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (2-5 e^x+5 x\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )}{\left (\left (-2 x-3 x^2+5 x^3+e^x \left (5 x-5 x^2\right )\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (-2 x+5 e^x x-5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )} \, dx=-\log (x)+\log \left (\log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )\right ) \]
[Out]
\[ \int \frac {-5 x+5 e^x x+\left (-2+e^x (5-5 x)-3 x+5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (\left (2+3 x-5 x^2+e^x (-5+5 x)\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (2-5 e^x+5 x\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )}{\left (\left (-2 x-3 x^2+5 x^3+e^x \left (5 x-5 x^2\right )\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (-2 x+5 e^x x-5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )} \, dx=\int \frac {-5 x+5 e^x x+\left (-2+e^x (5-5 x)-3 x+5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (\left (2+3 x-5 x^2+e^x (-5+5 x)\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (2-5 e^x+5 x\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )}{\left (\left (-2 x-3 x^2+5 x^3+e^x \left (5 x-5 x^2\right )\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (-2 x+5 e^x x-5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {5 x-5 e^x x+\left (-2+5 e^x-5 x\right ) (-1+x) \log \left (-\frac {2}{5}+e^x-x\right )-\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}{x \left (2-5 e^x+5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (1-x+\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx \\ & = \int \left (\frac {-3+5 x}{\left (2-5 e^x+5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}+\frac {-x-\log \left (-\frac {2}{5}+e^x-x\right )+x \log \left (-\frac {2}{5}+e^x-x\right )+\log \left (-\frac {2}{5}+e^x-x\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )-x \log \left (-\frac {2}{5}+e^x-x\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )+\log \left (-\frac {2}{5}+e^x-x\right ) \log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}{x \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}\right ) \, dx \\ & = \int \frac {-3+5 x}{\left (2-5 e^x+5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx+\int \frac {-x-\log \left (-\frac {2}{5}+e^x-x\right )+x \log \left (-\frac {2}{5}+e^x-x\right )+\log \left (-\frac {2}{5}+e^x-x\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )-x \log \left (-\frac {2}{5}+e^x-x\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )+\log \left (-\frac {2}{5}+e^x-x\right ) \log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}{x \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx \\ & = \int \left (\frac {3}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}-\frac {5 x}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}\right ) \, dx+\int \frac {x-\log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x+\left (1-x+\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )\right )}{x \log \left (-\frac {2}{5}+e^x-x\right ) \left (1-x+\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx \\ & = 3 \int \frac {1}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx-5 \int \frac {x}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx+\int \left (-\frac {1}{x}+\frac {-x-\log \left (-\frac {2}{5}+e^x-x\right )+x \log \left (-\frac {2}{5}+e^x-x\right )}{x \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}\right ) \, dx \\ & = -\log (x)+3 \int \frac {1}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx-5 \int \frac {x}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx+\int \frac {-x-\log \left (-\frac {2}{5}+e^x-x\right )+x \log \left (-\frac {2}{5}+e^x-x\right )}{x \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx \\ & = -\log (x)+3 \int \frac {1}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx-5 \int \frac {x}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx+\int \left (\frac {1}{\left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}-\frac {1}{x \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}-\frac {1}{\log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )}\right ) \, dx \\ & = -\log (x)+3 \int \frac {1}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx-5 \int \frac {x}{\left (-2+5 e^x-5 x\right ) \log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx+\int \frac {1}{\left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx-\int \frac {1}{x \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx-\int \frac {1}{\log \left (-\frac {2}{5}+e^x-x\right ) \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )} \, dx \\ \end{align*}
Time = 0.17 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {-5 x+5 e^x x+\left (-2+e^x (5-5 x)-3 x+5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (\left (2+3 x-5 x^2+e^x (-5+5 x)\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (2-5 e^x+5 x\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )}{\left (\left (-2 x-3 x^2+5 x^3+e^x \left (5 x-5 x^2\right )\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (-2 x+5 e^x x-5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )} \, dx=-\log (x)+\log \left (\log \left (-1+x-\log \left (x \log \left (-\frac {2}{5}+e^x-x\right )\right )\right )\right ) \]
[In]
[Out]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.08 (sec) , antiderivative size = 92, normalized size of antiderivative = 3.54
\[-\ln \left (x \right )+\ln \left (\ln \left (-\ln \left (x \right )-\ln \left (\ln \left ({\mathrm e}^{x}-x -\frac {2}{5}\right )\right )+\frac {i \pi \,\operatorname {csgn}\left (i x \ln \left ({\mathrm e}^{x}-x -\frac {2}{5}\right )\right ) \left (-\operatorname {csgn}\left (i x \ln \left ({\mathrm e}^{x}-x -\frac {2}{5}\right )\right )+\operatorname {csgn}\left (i x \right )\right ) \left (-\operatorname {csgn}\left (i x \ln \left ({\mathrm e}^{x}-x -\frac {2}{5}\right )\right )+\operatorname {csgn}\left (i \ln \left ({\mathrm e}^{x}-x -\frac {2}{5}\right )\right )\right )}{2}+x -1\right )\right )\]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.88 \[ \int \frac {-5 x+5 e^x x+\left (-2+e^x (5-5 x)-3 x+5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (\left (2+3 x-5 x^2+e^x (-5+5 x)\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (2-5 e^x+5 x\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )}{\left (\left (-2 x-3 x^2+5 x^3+e^x \left (5 x-5 x^2\right )\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (-2 x+5 e^x x-5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )} \, dx=-\log \left (x\right ) + \log \left (\log \left (x - \log \left (x \log \left (-x + e^{x} - \frac {2}{5}\right )\right ) - 1\right )\right ) \]
[In]
[Out]
Timed out. \[ \int \frac {-5 x+5 e^x x+\left (-2+e^x (5-5 x)-3 x+5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (\left (2+3 x-5 x^2+e^x (-5+5 x)\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (2-5 e^x+5 x\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )}{\left (\left (-2 x-3 x^2+5 x^3+e^x \left (5 x-5 x^2\right )\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (-2 x+5 e^x x-5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )} \, dx=\text {Timed out} \]
[In]
[Out]
none
Time = 0.53 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {-5 x+5 e^x x+\left (-2+e^x (5-5 x)-3 x+5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (\left (2+3 x-5 x^2+e^x (-5+5 x)\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (2-5 e^x+5 x\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )}{\left (\left (-2 x-3 x^2+5 x^3+e^x \left (5 x-5 x^2\right )\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (-2 x+5 e^x x-5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )} \, dx=-\log \left (x\right ) + \log \left (\log \left (x - \log \left (x\right ) - \log \left (-\log \left (5\right ) + \log \left (-5 \, x + 5 \, e^{x} - 2\right )\right ) - 1\right )\right ) \]
[In]
[Out]
none
Time = 2.32 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {-5 x+5 e^x x+\left (-2+e^x (5-5 x)-3 x+5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (\left (2+3 x-5 x^2+e^x (-5+5 x)\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (2-5 e^x+5 x\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )}{\left (\left (-2 x-3 x^2+5 x^3+e^x \left (5 x-5 x^2\right )\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (-2 x+5 e^x x-5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )} \, dx=-\log \left (x\right ) + \log \left (\log \left (x - \log \left (x\right ) - \log \left (-\log \left (5\right ) + \log \left (-5 \, x + 5 \, e^{x} - 2\right )\right ) - 1\right )\right ) \]
[In]
[Out]
Time = 12.35 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.88 \[ \int \frac {-5 x+5 e^x x+\left (-2+e^x (5-5 x)-3 x+5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (\left (2+3 x-5 x^2+e^x (-5+5 x)\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (2-5 e^x+5 x\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )}{\left (\left (-2 x-3 x^2+5 x^3+e^x \left (5 x-5 x^2\right )\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )+\left (-2 x+5 e^x x-5 x^2\right ) \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right ) \log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right ) \log \left (-1+x-\log \left (x \log \left (\frac {1}{5} \left (-2+5 e^x-5 x\right )\right )\right )\right )} \, dx=\ln \left (\ln \left (x-\ln \left (x\,\ln \left ({\mathrm {e}}^x-x-\frac {2}{5}\right )\right )-1\right )\right )-\ln \left (x\right ) \]
[In]
[Out]