Integrand size = 231, antiderivative size = 38 \[ \int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x^3-10 x^4+x^5+\left (25 x-10 x^2+x^3\right ) \log (x)} \, dx=-2-x+\frac {2 x}{5-x}+\left (-e^x+5 \log \left (\frac {1}{2} \left (x+\frac {\log (x)}{x}\right )\right )\right )^2 \]
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\[ \int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x^3-10 x^4+x^5+\left (25 x-10 x^2+x^3\right ) \log (x)} \, dx=\int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x^3-10 x^4+x^5+\left (25 x-10 x^2+x^3\right ) \log (x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(5-x)^2 x \left (x^2+\log (x)\right )} \, dx \\ & = \int \left (2 e^{2 x}-\frac {15 x^2}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {10 x^3}{(-5+x)^2 \left (x^2+\log (x)\right )}-\frac {x^4}{(-5+x)^2 \left (x^2+\log (x)\right )}-\frac {15 \log (x)}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {10 x \log (x)}{(-5+x)^2 \left (x^2+\log (x)\right )}-\frac {x^2 \log (x)}{(-5+x)^2 \left (x^2+\log (x)\right )}-\frac {500 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {1250 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 x \left (x^2+\log (x)\right )}+\frac {1300 x \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}-\frac {500 x^2 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {50 x^3 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {500 \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}-\frac {1250 \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 x \left (x^2+\log (x)\right )}-\frac {50 x \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}-\frac {10 e^x \left (1+x^2-\log (x)+x^3 \log \left (\frac {x^2+\log (x)}{2 x}\right )+x \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )\right )}{x \left (x^2+\log (x)\right )}\right ) \, dx \\ & = 2 \int e^{2 x} \, dx+10 \int \frac {x^3}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+10 \int \frac {x \log (x)}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-10 \int \frac {e^x \left (1+x^2-\log (x)+x^3 \log \left (\frac {x^2+\log (x)}{2 x}\right )+x \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )\right )}{x \left (x^2+\log (x)\right )} \, dx-15 \int \frac {x^2}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-15 \int \frac {\log (x)}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+50 \int \frac {x^3 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-50 \int \frac {x \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-500 \int \frac {x^2 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+500 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+1250 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 x \left (x^2+\log (x)\right )} \, dx-1250 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 x \left (x^2+\log (x)\right )} \, dx+1300 \int \frac {x \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-\int \frac {x^4}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-\int \frac {x^2 \log (x)}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx \\ & = e^{2 x}-\frac {10 e^x \left (x^3 \log \left (\frac {x^2+\log (x)}{2 x}\right )+x \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )\right )}{x \left (x^2+\log (x)\right )}+10 \int \left (\frac {10}{x^2+\log (x)}+\frac {125}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {75}{(-5+x) \left (x^2+\log (x)\right )}+\frac {x}{x^2+\log (x)}\right ) \, dx+10 \int \left (\frac {x}{(-5+x)^2}-\frac {x^3}{(-5+x)^2 \left (x^2+\log (x)\right )}\right ) \, dx-15 \int \left (\frac {1}{x^2+\log (x)}+\frac {25}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {10}{(-5+x) \left (x^2+\log (x)\right )}\right ) \, dx-15 \int \left (\frac {1}{(-5+x)^2}-\frac {x^2}{(-5+x)^2 \left (x^2+\log (x)\right )}\right ) \, dx+50 \int \left (\frac {10 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{x^2+\log (x)}+\frac {125 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {75 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )}+\frac {x \log \left (\frac {x^2+\log (x)}{2 x}\right )}{x^2+\log (x)}\right ) \, dx-50 \int \left (\frac {5 \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )}\right ) \, dx-500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+500 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-500 \int \left (\frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{x^2+\log (x)}+\frac {25 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {10 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )}\right ) \, dx+1250 \int \left (\frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{5 (-5+x)^2 \left (x^2+\log (x)\right )}-\frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 (-5+x) \left (x^2+\log (x)\right )}+\frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x \left (x^2+\log (x)\right )}\right ) \, dx-1250 \int \left (\frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{5 (-5+x)^2 \left (x^2+\log (x)\right )}-\frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 (-5+x) \left (x^2+\log (x)\right )}+\frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x \left (x^2+\log (x)\right )}\right ) \, dx+1300 \int \left (\frac {5 \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )}\right ) \, dx-\int \left (\frac {75}{x^2+\log (x)}+\frac {625}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {500}{(-5+x) \left (x^2+\log (x)\right )}+\frac {10 x}{x^2+\log (x)}+\frac {x^2}{x^2+\log (x)}\right ) \, dx-\int \left (\frac {x^2}{(-5+x)^2}-\frac {x^4}{(-5+x)^2 \left (x^2+\log (x)\right )}\right ) \, dx \\ & = e^{2 x}-\frac {15}{5-x}-\frac {10 e^x \left (x^3 \log \left (\frac {x^2+\log (x)}{2 x}\right )+x \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )\right )}{x \left (x^2+\log (x)\right )}+10 \int \frac {x}{(-5+x)^2} \, dx-10 \int \frac {x^3}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-15 \int \frac {1}{x^2+\log (x)} \, dx+15 \int \frac {x^2}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-50 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx+50 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{x \left (x^2+\log (x)\right )} \, dx+50 \int \frac {x \log \left (\frac {x^2+\log (x)}{2 x}\right )}{x^2+\log (x)} \, dx-50 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{x \left (x^2+\log (x)\right )} \, dx-75 \int \frac {1}{x^2+\log (x)} \, dx+100 \int \frac {1}{x^2+\log (x)} \, dx-150 \int \frac {1}{(-5+x) \left (x^2+\log (x)\right )} \, dx+250 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-2 \left (250 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx\right )-375 \int \frac {1}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-500 \int \frac {1}{(-5+x) \left (x^2+\log (x)\right )} \, dx-500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+500 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-625 \int \frac {1}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+750 \int \frac {1}{(-5+x) \left (x^2+\log (x)\right )} \, dx+1250 \int \frac {1}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+1300 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx+3750 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx-5000 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx+6250 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+6500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-12500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-\int \frac {x^2}{(-5+x)^2} \, dx-\int \frac {x^2}{x^2+\log (x)} \, dx+\int \frac {x^4}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx \\ & = e^{2 x}-\frac {15}{5-x}-\frac {10 e^x \left (x^3 \log \left (\frac {x^2+\log (x)}{2 x}\right )+x \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )\right )}{x \left (x^2+\log (x)\right )}+10 \int \left (\frac {5}{(-5+x)^2}+\frac {1}{-5+x}\right ) \, dx-10 \int \left (\frac {10}{x^2+\log (x)}+\frac {125}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {75}{(-5+x) \left (x^2+\log (x)\right )}+\frac {x}{x^2+\log (x)}\right ) \, dx-15 \int \frac {1}{x^2+\log (x)} \, dx+15 \int \left (\frac {1}{x^2+\log (x)}+\frac {25}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {10}{(-5+x) \left (x^2+\log (x)\right )}\right ) \, dx-50 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx+50 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{x \left (x^2+\log (x)\right )} \, dx+50 \int \frac {x \log \left (\frac {x^2+\log (x)}{2 x}\right )}{x^2+\log (x)} \, dx-50 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{x \left (x^2+\log (x)\right )} \, dx-75 \int \frac {1}{x^2+\log (x)} \, dx+100 \int \frac {1}{x^2+\log (x)} \, dx-150 \int \frac {1}{(-5+x) \left (x^2+\log (x)\right )} \, dx+250 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-2 \left (250 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx\right )-375 \int \frac {1}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-500 \int \frac {1}{(-5+x) \left (x^2+\log (x)\right )} \, dx-500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+500 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-625 \int \frac {1}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+750 \int \frac {1}{(-5+x) \left (x^2+\log (x)\right )} \, dx+1250 \int \frac {1}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+1300 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx+3750 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx-5000 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx+6250 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+6500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-12500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-\int \left (1+\frac {25}{(-5+x)^2}+\frac {10}{-5+x}\right ) \, dx-\int \frac {x^2}{x^2+\log (x)} \, dx+\int \left (\frac {75}{x^2+\log (x)}+\frac {625}{(-5+x)^2 \left (x^2+\log (x)\right )}+\frac {500}{(-5+x) \left (x^2+\log (x)\right )}+\frac {10 x}{x^2+\log (x)}+\frac {x^2}{x^2+\log (x)}\right ) \, dx \\ & = e^{2 x}+\frac {10}{5-x}-x-\frac {10 e^x \left (x^3 \log \left (\frac {x^2+\log (x)}{2 x}\right )+x \log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )\right )}{x \left (x^2+\log (x)\right )}-50 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx+50 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{x \left (x^2+\log (x)\right )} \, dx+50 \int \frac {x \log \left (\frac {x^2+\log (x)}{2 x}\right )}{x^2+\log (x)} \, dx-50 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{x \left (x^2+\log (x)\right )} \, dx+250 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-2 \left (250 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx\right )-500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+500 \int \frac {\log (x) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+1300 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx+3750 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx-5000 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x) \left (x^2+\log (x)\right )} \, dx+6250 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx+6500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx-12500 \int \frac {\log \left (\frac {x^2+\log (x)}{2 x}\right )}{(-5+x)^2 \left (x^2+\log (x)\right )} \, dx \\ \end{align*}
Time = 0.24 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.39 \[ \int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x^3-10 x^4+x^5+\left (25 x-10 x^2+x^3\right ) \log (x)} \, dx=e^{2 x}-\frac {10}{-5+x}-x-10 e^x \log \left (\frac {x^2+\log (x)}{2 x}\right )+25 \log ^2\left (\frac {x^2+\log (x)}{2 x}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(93\) vs. \(2(36)=72\).
Time = 15.28 (sec) , antiderivative size = 94, normalized size of antiderivative = 2.47
method | result | size |
parallelrisch | \(-\frac {-150-10 x \,{\mathrm e}^{2 x}+100 x \,{\mathrm e}^{x} \ln \left (\frac {\ln \left (x \right )+x^{2}}{2 x}\right )-250 \ln \left (\frac {\ln \left (x \right )+x^{2}}{2 x}\right )^{2} x +10 x^{2}+50 \,{\mathrm e}^{2 x}-500 \ln \left (\frac {\ln \left (x \right )+x^{2}}{2 x}\right ) {\mathrm e}^{x}+1250 \ln \left (\frac {\ln \left (x \right )+x^{2}}{2 x}\right )^{2}}{10 \left (-5+x \right )}\) | \(94\) |
risch | \(\text {Expression too large to display}\) | \(1971\) |
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Time = 0.26 (sec) , antiderivative size = 62, normalized size of antiderivative = 1.63 \[ \int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x^3-10 x^4+x^5+\left (25 x-10 x^2+x^3\right ) \log (x)} \, dx=-\frac {10 \, {\left (x - 5\right )} e^{x} \log \left (\frac {x^{2} + \log \left (x\right )}{2 \, x}\right ) - 25 \, {\left (x - 5\right )} \log \left (\frac {x^{2} + \log \left (x\right )}{2 \, x}\right )^{2} + x^{2} - {\left (x - 5\right )} e^{\left (2 \, x\right )} - 5 \, x + 10}{x - 5} \]
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Time = 4.83 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.21 \[ \int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x^3-10 x^4+x^5+\left (25 x-10 x^2+x^3\right ) \log (x)} \, dx=- x + e^{2 x} - 10 e^{x} \log {\left (\frac {\frac {x^{2}}{2} + \frac {\log {\left (x \right )}}{2}}{x} \right )} + 25 \log {\left (\frac {\frac {x^{2}}{2} + \frac {\log {\left (x \right )}}{2}}{x} \right )}^{2} - \frac {10}{x - 5} \]
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Leaf count of result is larger than twice the leaf count of optimal. 111 vs. \(2 (32) = 64\).
Time = 0.34 (sec) , antiderivative size = 111, normalized size of antiderivative = 2.92 \[ \int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x^3-10 x^4+x^5+\left (25 x-10 x^2+x^3\right ) \log (x)} \, dx=\frac {25 \, {\left (x - 5\right )} \log \left (x^{2} + \log \left (x\right )\right )^{2} + 25 \, {\left (x - 5\right )} \log \left (x\right )^{2} - x^{2} + {\left (x - 5\right )} e^{\left (2 \, x\right )} + 10 \, {\left (x \log \left (2\right ) + {\left (x - 5\right )} \log \left (x\right ) - 5 \, \log \left (2\right )\right )} e^{x} - 10 \, {\left ({\left (x - 5\right )} e^{x} + 5 \, x \log \left (2\right ) + 5 \, {\left (x - 5\right )} \log \left (x\right ) - 25 \, \log \left (2\right )\right )} \log \left (x^{2} + \log \left (x\right )\right ) + 50 \, {\left (x \log \left (2\right ) - 5 \, \log \left (2\right )\right )} \log \left (x\right ) + 5 \, x - 10}{x - 5} \]
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Leaf count of result is larger than twice the leaf count of optimal. 172 vs. \(2 (32) = 64\).
Time = 0.31 (sec) , antiderivative size = 172, normalized size of antiderivative = 4.53 \[ \int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x^3-10 x^4+x^5+\left (25 x-10 x^2+x^3\right ) \log (x)} \, dx=\frac {10 \, x e^{x} \log \left (2\right ) - 10 \, x e^{x} \log \left (x^{2} + \log \left (x\right )\right ) - 50 \, x \log \left (2\right ) \log \left (x^{2} + \log \left (x\right )\right ) + 25 \, x \log \left (x^{2} + \log \left (x\right )\right )^{2} + 10 \, x e^{x} \log \left (x\right ) + 50 \, x \log \left (2\right ) \log \left (x\right ) - 50 \, x \log \left (x^{2} + \log \left (x\right )\right ) \log \left (x\right ) + 25 \, x \log \left (x\right )^{2} - x^{2} + x e^{\left (2 \, x\right )} - 50 \, e^{x} \log \left (2\right ) + 50 \, e^{x} \log \left (x^{2} + \log \left (x\right )\right ) + 250 \, \log \left (2\right ) \log \left (x^{2} + \log \left (x\right )\right ) - 125 \, \log \left (x^{2} + \log \left (x\right )\right )^{2} - 50 \, e^{x} \log \left (x\right ) - 250 \, \log \left (2\right ) \log \left (x\right ) + 250 \, \log \left (x^{2} + \log \left (x\right )\right ) \log \left (x\right ) - 125 \, \log \left (x\right )^{2} + 5 \, x - 5 \, e^{\left (2 \, x\right )} - 10}{x - 5} \]
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Time = 9.86 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.39 \[ \int \frac {-15 x^3+10 x^4-x^5+e^x \left (-250+100 x-260 x^2+100 x^3-10 x^4\right )+e^{2 x} \left (50 x^3-20 x^4+2 x^5\right )+\left (-15 x+10 x^2-x^3+e^x \left (250-100 x+10 x^2\right )+e^{2 x} \left (50 x-20 x^2+2 x^3\right )\right ) \log (x)+\left (1250-500 x+1300 x^2-500 x^3+50 x^4+e^x \left (-250 x^3+100 x^4-10 x^5\right )+\left (-1250+500 x-50 x^2+e^x \left (-250 x+100 x^2-10 x^3\right )\right ) \log (x)\right ) \log \left (\frac {x^2+\log (x)}{2 x}\right )}{25 x^3-10 x^4+x^5+\left (25 x-10 x^2+x^3\right ) \log (x)} \, dx={\mathrm {e}}^{2\,x}-x-\frac {10}{x-5}-10\,{\mathrm {e}}^x\,\ln \left (\frac {\frac {\ln \left (x\right )}{2}+\frac {x^2}{2}}{x}\right )+25\,{\ln \left (\frac {\frac {\ln \left (x\right )}{2}+\frac {x^2}{2}}{x}\right )}^2 \]
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