Integrand size = 172, antiderivative size = 28 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=3-\left (-x+e^5 (4+x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )^2 \]
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\[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=\int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \left (x-e^5 (4+x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right ) \left (e^5 (4+x)+\log (x) \left (-x+e^5 \left (-4+3 x+x^2\right )+e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )\right )\right )}{x \log (x)} \, dx \\ & = 2 \int \frac {\left (x-e^5 (4+x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right ) \left (e^5 (4+x)+\log (x) \left (-x+e^5 \left (-4+3 x+x^2\right )+e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )\right )\right )}{x \log (x)} \, dx \\ & = 2 \int \left (\frac {4 e^5+e^5 x-4 e^5 \log (x)-\left (1-3 e^5\right ) x \log (x)+e^5 x^2 \log (x)}{\log (x)}+\frac {e^5 \left (-16 e^5-8 e^5 x-e^5 x^2+16 e^5 \log (x)+4 \left (1-2 e^5\right ) x \log (x)+2 \left (1-\frac {7 e^5}{2}\right ) x^2 \log (x)-e^5 x^3 \log (x)\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)}-e^{10} (4+x) \log ^2\left (\frac {5 e^x \log (x)}{x}\right )\right ) \, dx \\ & = 2 \int \frac {4 e^5+e^5 x-4 e^5 \log (x)-\left (1-3 e^5\right ) x \log (x)+e^5 x^2 \log (x)}{\log (x)} \, dx+\left (2 e^5\right ) \int \frac {\left (-16 e^5-8 e^5 x-e^5 x^2+16 e^5 \log (x)+4 \left (1-2 e^5\right ) x \log (x)+2 \left (1-\frac {7 e^5}{2}\right ) x^2 \log (x)-e^5 x^3 \log (x)\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (2 e^{10}\right ) \int (4+x) \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx \\ & = 2 \int \left (-x+e^5 \left (-4+3 x+x^2\right )+\frac {e^5 (4+x)}{\log (x)}\right ) \, dx+\left (2 e^5\right ) \int \frac {\left (-e^5 (4+x)^2-\left (-2 x (2+x)+e^5 (-1+x) (4+x)^2\right ) \log (x)\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (2 e^{10}\right ) \int \left (4 \log ^2\left (\frac {5 e^x \log (x)}{x}\right )+x \log ^2\left (\frac {5 e^x \log (x)}{x}\right )\right ) \, dx \\ & = -x^2+\left (2 e^5\right ) \int \left (-4+3 x+x^2\right ) \, dx+\left (2 e^5\right ) \int \frac {4+x}{\log (x)} \, dx+\left (2 e^5\right ) \int \left (4 \left (1-2 e^5\right ) \log \left (\frac {5 e^x \log (x)}{x}\right )+\frac {16 e^5 \log \left (\frac {5 e^x \log (x)}{x}\right )}{x}+2 \left (1-\frac {7 e^5}{2}\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )-e^5 x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {8 e^5 \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)}-\frac {16 e^5 \log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)}-\frac {e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)}\right ) \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx \\ & = -8 e^5 x-x^2+3 e^5 x^2+\frac {2 e^5 x^3}{3}+\left (2 e^5\right ) \int \left (\frac {4}{\log (x)}+\frac {x}{\log (x)}\right ) \, dx-\left (2 e^{10}\right ) \int x^2 \log \left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (16 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx+\left (2 e^5 \left (2-7 e^5\right )\right ) \int x \log \left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (8 e^5 \left (1-2 e^5\right )\right ) \int \log \left (\frac {5 e^x \log (x)}{x}\right ) \, dx \\ & = -8 e^5 x-x^2+3 e^5 x^2+\frac {2 e^5 x^3}{3}+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\left (2 e^5\right ) \int \frac {x}{\log (x)} \, dx+\left (8 e^5\right ) \int \frac {1}{\log (x)} \, dx+\left (2 e^{10}\right ) \int \frac {x^2 (1+(-1+x) \log (x))}{3 \log (x)} \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {(1+(-1+x) \log (x)) \operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (2 e^5 \left (2-7 e^5\right )\right ) \int \frac {x (1+(-1+x) \log (x))}{2 \log (x)} \, dx-\left (8 e^5 \left (1-2 e^5\right )\right ) \int \left (-1+x+\frac {1}{\log (x)}\right ) \, dx \\ & = -8 e^5 x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\left (2 e^5\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )+\frac {1}{3} \left (2 e^{10}\right ) \int \frac {x^2 (1+(-1+x) \log (x))}{\log (x)} \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \left (\operatorname {LogIntegral}(x)-\frac {\operatorname {LogIntegral}(x)}{x}+\frac {\operatorname {LogIntegral}(x)}{x \log (x)}\right ) \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \frac {x (1+(-1+x) \log (x))}{\log (x)} \, dx-\left (8 e^5 \left (1-2 e^5\right )\right ) \int \frac {1}{\log (x)} \, dx \\ & = -8 e^5 x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\frac {1}{3} \left (2 e^{10}\right ) \int \left ((-1+x) x^2+\frac {x^2}{\log (x)}\right ) \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \operatorname {LogIntegral}(x) \, dx-\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x} \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int x \left (-1+x+\frac {1}{\log (x)}\right ) \, dx \\ & = -8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))-16 e^{10} \operatorname {ExpIntegralEi}(2 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)+16 e^{10} x \operatorname {LogIntegral}(x)-16 e^{10} \log (x) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\frac {1}{3} \left (2 e^{10}\right ) \int (-1+x) x^2 \, dx+\frac {1}{3} \left (2 e^{10}\right ) \int \frac {x^2}{\log (x)} \, dx-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \left ((-1+x) x+\frac {x}{\log (x)}\right ) \, dx \\ & = -8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))-16 e^{10} \operatorname {ExpIntegralEi}(2 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)+16 e^{10} x \operatorname {LogIntegral}(x)-16 e^{10} \log (x) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)+\frac {1}{3} \left (2 e^{10}\right ) \int \left (-x^2+x^3\right ) \, dx+\frac {1}{3} \left (2 e^{10}\right ) \text {Subst}\left (\int \frac {e^{3 x}}{x} \, dx,x,\log (x)\right )-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int (-1+x) x \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \frac {x}{\log (x)} \, dx \\ & = -8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}-\frac {2 e^{10} x^3}{9}+\frac {e^{10} x^4}{6}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))-16 e^{10} \operatorname {ExpIntegralEi}(2 \log (x))+\frac {2}{3} e^{10} \operatorname {ExpIntegralEi}(3 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)+16 e^{10} x \operatorname {LogIntegral}(x)-16 e^{10} \log (x) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \int \left (-x+x^2\right ) \, dx-\left (e^5 \left (2-7 e^5\right )\right ) \text {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right ) \\ & = -8 e^5 x+16 e^{10} x+8 e^5 \left (1-2 e^5\right ) x-x^2+3 e^5 x^2+\frac {1}{2} e^5 \left (2-7 e^5\right ) x^2-4 e^5 \left (1-2 e^5\right ) x^2+\frac {2 e^5 x^3}{3}-\frac {2 e^{10} x^3}{9}-\frac {1}{3} e^5 \left (2-7 e^5\right ) x^3+\frac {e^{10} x^4}{6}+2 e^5 \operatorname {ExpIntegralEi}(2 \log (x))-16 e^{10} \operatorname {ExpIntegralEi}(2 \log (x))-e^5 \left (2-7 e^5\right ) \operatorname {ExpIntegralEi}(2 \log (x))+\frac {2}{3} e^{10} \operatorname {ExpIntegralEi}(3 \log (x))+8 e^5 \left (1-2 e^5\right ) x \log \left (\frac {5 e^x \log (x)}{x}\right )+e^5 \left (2-7 e^5\right ) x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-\frac {2}{3} e^{10} x^3 \log \left (\frac {5 e^x \log (x)}{x}\right )+8 e^5 \operatorname {LogIntegral}(x)-8 e^5 \left (1-2 e^5\right ) \operatorname {LogIntegral}(x)+16 e^{10} x \operatorname {LogIntegral}(x)-16 e^{10} \log (x) \operatorname {LogIntegral}(x)-16 e^{10} \log \left (\frac {5 e^x \log (x)}{x}\right ) \operatorname {LogIntegral}(x)-\left (2 e^{10}\right ) \int \frac {x \log \left (\frac {5 e^x \log (x)}{x}\right )}{\log (x)} \, dx-\left (2 e^{10}\right ) \int x \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx-\left (8 e^{10}\right ) \int \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \, dx+\left (16 e^{10}\right ) \int \frac {\operatorname {LogIntegral}(x)}{x \log (x)} \, dx+\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x} \, dx-\left (32 e^{10}\right ) \int \frac {\log \left (\frac {5 e^x \log (x)}{x}\right )}{x \log (x)} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(180\) vs. \(2(28)=56\).
Time = 0.69 (sec) , antiderivative size = 180, normalized size of antiderivative = 6.43 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=-x^2+16 e^{10} x^2-16 e^{10} \log ^2\left (\frac {\log (x)}{x}\right )-32 e^{10} \log (x) \left (x+\log \left (\frac {\log (x)}{x}\right )-\log \left (\frac {5 e^x \log (x)}{x}\right )\right )+32 e^{10} \log (\log (x)) \left (x+\log \left (\frac {\log (x)}{x}\right )-\log \left (\frac {5 e^x \log (x)}{x}\right )\right )+8 e^5 x \log \left (\frac {5 e^x \log (x)}{x}\right )-32 e^{10} x \log \left (\frac {5 e^x \log (x)}{x}\right )+2 e^5 x^2 \log \left (\frac {5 e^x \log (x)}{x}\right )-8 e^{10} x \log ^2\left (\frac {5 e^x \log (x)}{x}\right )-e^{10} x^2 \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(185\) vs. \(2(28)=56\).
Time = 16.49 (sec) , antiderivative size = 186, normalized size of antiderivative = 6.64
method | result | size |
parallelrisch | \(\frac {-\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{4} {\mathrm e}^{10} x^{2}+2 \,{\mathrm e}^{\ln \left (\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )\right )+5} \ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{2} x^{2}-8 \ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{4} {\mathrm e}^{10} x -\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{2} x^{2}+8 \,{\mathrm e}^{\ln \left (\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )\right )+5} \ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{2} x -16 \ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{4} {\mathrm e}^{10}}{\ln \left (\frac {5 \,{\mathrm e}^{x} \ln \left (x \right )}{x}\right )^{2}}\) | \(186\) |
risch | \(\text {Expression too large to display}\) | \(5910\) |
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Time = 0.27 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.82 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=-{\left (x^{2} + 8 \, x + 16\right )} e^{10} \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right )^{2} + 2 \, {\left (x^{2} + 4 \, x\right )} e^{5} \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right ) - x^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (22) = 44\).
Time = 0.34 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.25 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=- x^{2} + \left (2 x^{2} e^{5} + 8 x e^{5}\right ) \log {\left (\frac {5 e^{x} \log {\left (x \right )}}{x} \right )} + \left (- x^{2} e^{10} - 8 x e^{10} - 16 e^{10}\right ) \log {\left (\frac {5 e^{x} \log {\left (x \right )}}{x} \right )}^{2} \]
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\[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=\int { -\frac {2 \, {\left (x^{2} \log \left (x\right ) \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right ) + {\left ({\left (x^{2} + 4 \, x\right )} \log \left (x\right ) \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right ) + x^{2} + {\left (x^{3} + 7 \, x^{2} + 8 \, x - 16\right )} \log \left (x\right ) + 8 \, x + 16\right )} e^{\left (2 \, \log \left (\log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right )\right ) + 10\right )} - {\left (2 \, {\left (x^{2} + 2 \, x\right )} \log \left (x\right ) \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right ) + x^{2} + {\left (x^{3} + 3 \, x^{2} - 4 \, x\right )} \log \left (x\right ) + 4 \, x\right )} e^{\left (\log \left (\log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right )\right ) + 5\right )}\right )}}{x \log \left (x\right ) \log \left (\frac {5 \, e^{x} \log \left (x\right )}{x}\right )} \,d x } \]
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Leaf count of result is larger than twice the leaf count of optimal. 338 vs. \(2 (28) = 56\).
Time = 0.35 (sec) , antiderivative size = 338, normalized size of antiderivative = 12.07 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=-x^{4} e^{10} - 2 \, x^{3} e^{10} \log \left (5\right ) - x^{2} e^{10} \log \left (5\right )^{2} + 2 \, x^{3} e^{10} \log \left (x\right ) + 2 \, x^{2} e^{10} \log \left (5\right ) \log \left (x\right ) - x^{2} e^{10} \log \left (x\right )^{2} - 2 \, x^{3} e^{10} \log \left (\log \left (x\right )\right ) - 2 \, x^{2} e^{10} \log \left (5\right ) \log \left (\log \left (x\right )\right ) + 2 \, x^{2} e^{10} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - x^{2} e^{10} \log \left (\log \left (x\right )\right )^{2} - 8 \, x^{3} e^{10} + 2 \, x^{3} e^{5} - 16 \, x^{2} e^{10} \log \left (5\right ) + 2 \, x^{2} e^{5} \log \left (5\right ) - 8 \, x e^{10} \log \left (5\right )^{2} + 16 \, x^{2} e^{10} \log \left (x\right ) - 2 \, x^{2} e^{5} \log \left (x\right ) + 16 \, x e^{10} \log \left (5\right ) \log \left (x\right ) - 8 \, x e^{10} \log \left (x\right )^{2} - 16 \, x^{2} e^{10} \log \left (\log \left (x\right )\right ) + 2 \, x^{2} e^{5} \log \left (\log \left (x\right )\right ) - 16 \, x e^{10} \log \left (5\right ) \log \left (\log \left (x\right )\right ) + 16 \, x e^{10} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 8 \, x e^{10} \log \left (\log \left (x\right )\right )^{2} - 16 \, x^{2} e^{10} + 8 \, x^{2} e^{5} - 32 \, x e^{10} \log \left (5\right ) + 8 \, x e^{5} \log \left (5\right ) + 32 \, x e^{10} \log \left (x\right ) - 8 \, x e^{5} \log \left (x\right ) + 32 \, e^{10} \log \left (5\right ) \log \left (x\right ) - 16 \, e^{10} \log \left (x\right )^{2} - 32 \, x e^{10} \log \left (\log \left (x\right )\right ) + 8 \, x e^{5} \log \left (\log \left (x\right )\right ) - 32 \, e^{10} \log \left (5\right ) \log \left (\log \left (x\right )\right ) + 32 \, e^{10} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 16 \, e^{10} \log \left (\log \left (x\right )\right )^{2} - x^{2} \]
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Time = 9.40 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {-2 x^2 \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )+e^{10} \log ^2\left (\frac {5 e^x \log (x)}{x}\right ) \left (-32-16 x-2 x^2+\left (32-16 x-14 x^2-2 x^3\right ) \log (x)+\left (-8 x-2 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )+e^5 \log \left (\frac {5 e^x \log (x)}{x}\right ) \left (8 x+2 x^2+\left (-8 x+6 x^2+2 x^3\right ) \log (x)+\left (8 x+4 x^2\right ) \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )\right )}{x \log (x) \log \left (\frac {5 e^x \log (x)}{x}\right )} \, dx=-{\left (4\,\ln \left (\frac {5\,{\mathrm {e}}^x\,\ln \left (x\right )}{x}\right )\,{\mathrm {e}}^5-x+x\,\ln \left (\frac {5\,{\mathrm {e}}^x\,\ln \left (x\right )}{x}\right )\,{\mathrm {e}}^5\right )}^2 \]
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