Integrand size = 175, antiderivative size = 28 \[ \int \frac {25 x^2+e^x \left (-100 e^{4/x}+96 x^2\right )+\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)+\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{-25 x^2+e^x \left (25 e^{4/x} x^2+95 x^3\right )+\left (-10 x^2+e^x \left (10 e^{4/x} x^2+39 x^3\right )\right ) \log (x)+\left (-x^2+e^x \left (e^{4/x} x^2+4 x^3\right )\right ) \log ^2(x)} \, dx=\log \left (e^{4/x}-e^{-x}+4 x-\frac {x}{5+\log (x)}\right ) \]
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\[ \int \frac {25 x^2+e^x \left (-100 e^{4/x}+96 x^2\right )+\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)+\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{-25 x^2+e^x \left (25 e^{4/x} x^2+95 x^3\right )+\left (-10 x^2+e^x \left (10 e^{4/x} x^2+39 x^3\right )\right ) \log (x)+\left (-x^2+e^x \left (e^{4/x} x^2+4 x^3\right )\right ) \log ^2(x)} \, dx=\int \frac {25 x^2+e^x \left (-100 e^{4/x}+96 x^2\right )+\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)+\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{-25 x^2+e^x \left (25 e^{4/x} x^2+95 x^3\right )+\left (-10 x^2+e^x \left (10 e^{4/x} x^2+39 x^3\right )\right ) \log (x)+\left (-x^2+e^x \left (e^{4/x} x^2+4 x^3\right )\right ) \log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-25 x^2-e^x \left (-100 e^{4/x}+96 x^2\right )-\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)-\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{x^2 (5+\log (x)) \left (5-5 e^{\frac {4}{x}+x}-19 e^x x+\log (x)-e^{\frac {4}{x}+x} \log (x)-4 e^x x \log (x)\right )} \, dx \\ & = \int \left (\frac {-100 e^{4/x}+96 x^2-40 e^{4/x} \log (x)+39 x^2 \log (x)-4 e^{4/x} \log ^2(x)+4 x^2 \log ^2(x)}{x^2 (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )}+\frac {-100 e^{4/x}+96 x^2+25 e^{4/x} x^2+95 x^3-40 e^{4/x} \log (x)+39 x^2 \log (x)+10 e^{4/x} x^2 \log (x)+39 x^3 \log (x)-4 e^{4/x} \log ^2(x)+4 x^2 \log ^2(x)+e^{4/x} x^2 \log ^2(x)+4 x^3 \log ^2(x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}\right ) \, dx \\ & = \int \frac {-100 e^{4/x}+96 x^2-40 e^{4/x} \log (x)+39 x^2 \log (x)-4 e^{4/x} \log ^2(x)+4 x^2 \log ^2(x)}{x^2 (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )} \, dx+\int \frac {-100 e^{4/x}+96 x^2+25 e^{4/x} x^2+95 x^3-40 e^{4/x} \log (x)+39 x^2 \log (x)+10 e^{4/x} x^2 \log (x)+39 x^3 \log (x)-4 e^{4/x} \log ^2(x)+4 x^2 \log ^2(x)+e^{4/x} x^2 \log ^2(x)+4 x^3 \log ^2(x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx \\ & = \int \left (\frac {96}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}+\frac {25 e^{4/x}}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}-\frac {100 e^{4/x}}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}+\frac {95 x}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}+\frac {39 \log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}+\frac {10 e^{4/x} \log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}-\frac {40 e^{4/x} \log (x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}+\frac {39 x \log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}+\frac {4 \log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}+\frac {e^{4/x} \log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}-\frac {4 e^{4/x} \log ^2(x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}+\frac {4 x \log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )}\right ) \, dx+\int \left (-\frac {4}{x^2}+\frac {380+96 x+156 \log (x)+39 x \log (x)+16 \log ^2(x)+4 x \log ^2(x)}{x (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )}\right ) \, dx \\ & = \frac {4}{x}+4 \int \frac {\log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx-4 \int \frac {e^{4/x} \log ^2(x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+4 \int \frac {x \log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+10 \int \frac {e^{4/x} \log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+25 \int \frac {e^{4/x}}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+39 \int \frac {\log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+39 \int \frac {x \log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx-40 \int \frac {e^{4/x} \log (x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+95 \int \frac {x}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+96 \int \frac {1}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx-100 \int \frac {e^{4/x}}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+\int \frac {e^{4/x} \log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+\int \frac {380+96 x+156 \log (x)+39 x \log (x)+16 \log ^2(x)+4 x \log ^2(x)}{x (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )} \, dx \\ & = \frac {4}{x}+4 \int \frac {\log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx-4 \int \frac {e^{4/x} \log ^2(x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+4 \int \frac {x \log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+10 \int \frac {e^{4/x} \log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+25 \int \frac {e^{4/x}}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+39 \int \frac {\log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+39 \int \frac {x \log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx-40 \int \frac {e^{4/x} \log (x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+95 \int \frac {x}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+96 \int \frac {1}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx-100 \int \frac {e^{4/x}}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+\int \frac {e^{4/x} \log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+\int \left (\frac {96}{(5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )}+\frac {380}{x (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )}+\frac {39 \log (x)}{(5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )}+\frac {156 \log (x)}{x (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )}+\frac {4 \log ^2(x)}{(5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )}+\frac {16 \log ^2(x)}{x (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )}\right ) \, dx \\ & = \frac {4}{x}+4 \int \frac {\log ^2(x)}{(5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )} \, dx+4 \int \frac {\log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx-4 \int \frac {e^{4/x} \log ^2(x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+4 \int \frac {x \log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+10 \int \frac {e^{4/x} \log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+16 \int \frac {\log ^2(x)}{x (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )} \, dx+25 \int \frac {e^{4/x}}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+39 \int \frac {\log (x)}{(5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )} \, dx+39 \int \frac {\log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+39 \int \frac {x \log (x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx-40 \int \frac {e^{4/x} \log (x)}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+95 \int \frac {x}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+96 \int \frac {1}{(5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )} \, dx+96 \int \frac {1}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx-100 \int \frac {e^{4/x}}{x^2 \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx+156 \int \frac {\log (x)}{x (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )} \, dx+380 \int \frac {1}{x (5+\log (x)) \left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right )} \, dx+\int \frac {e^{4/x} \log ^2(x)}{\left (5 e^{4/x}+19 x+e^{4/x} \log (x)+4 x \log (x)\right ) \left (-5+5 e^{\frac {4}{x}+x}+19 e^x x-\log (x)+e^{\frac {4}{x}+x} \log (x)+4 e^x x \log (x)\right )} \, dx \\ \end{align*}
Time = 0.16 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.93 \[ \int \frac {25 x^2+e^x \left (-100 e^{4/x}+96 x^2\right )+\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)+\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{-25 x^2+e^x \left (25 e^{4/x} x^2+95 x^3\right )+\left (-10 x^2+e^x \left (10 e^{4/x} x^2+39 x^3\right )\right ) \log (x)+\left (-x^2+e^x \left (e^{4/x} x^2+4 x^3\right )\right ) \log ^2(x)} \, dx=-x-\log (5+\log (x))+\log \left (5-5 e^{\frac {4}{x}+x}-19 e^x x+\log (x)-e^{\frac {4}{x}+x} \log (x)-4 e^x x \log (x)\right ) \]
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Time = 7.58 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.86
method | result | size |
parallelrisch | \(-\ln \left (5+\ln \left (x \right )\right )+\ln \left (x \,{\mathrm e}^{x} \ln \left (x \right )+\frac {{\mathrm e}^{\frac {4}{x}} \ln \left (x \right ) {\mathrm e}^{x}}{4}+\frac {19 \,{\mathrm e}^{x} x}{4}+\frac {5 \,{\mathrm e}^{\frac {4}{x}} {\mathrm e}^{x}}{4}-\frac {\ln \left (x \right )}{4}-\frac {5}{4}\right )-x\) | \(52\) |
risch | \(\ln \left (4 x +{\mathrm e}^{\frac {4}{x}}-{\mathrm e}^{-x}\right )+\ln \left (\ln \left (x \right )+\frac {19 \,{\mathrm e}^{x} x +5 \,{\mathrm e}^{\frac {x^{2}+4}{x}}-5}{4 \,{\mathrm e}^{x} x +{\mathrm e}^{\frac {x^{2}+4}{x}}-1}\right )-\ln \left (5+\ln \left (x \right )\right )\) | \(69\) |
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Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (26) = 52\).
Time = 0.28 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.75 \[ \int \frac {25 x^2+e^x \left (-100 e^{4/x}+96 x^2\right )+\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)+\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{-25 x^2+e^x \left (25 e^{4/x} x^2+95 x^3\right )+\left (-10 x^2+e^x \left (10 e^{4/x} x^2+39 x^3\right )\right ) \log (x)+\left (-x^2+e^x \left (e^{4/x} x^2+4 x^3\right )\right ) \log ^2(x)} \, dx=-x + \log \left (4 \, x + e^{\frac {4}{x}}\right ) + \log \left (\frac {{\left (19 \, x + 5 \, e^{\frac {4}{x}}\right )} e^{x} + {\left ({\left (4 \, x + e^{\frac {4}{x}}\right )} e^{x} - 1\right )} \log \left (x\right ) - 5}{{\left (4 \, x + e^{\frac {4}{x}}\right )} e^{x} - 1}\right ) + \log \left (\frac {{\left (4 \, x + e^{\frac {4}{x}}\right )} e^{x} - 1}{4 \, x + e^{\frac {4}{x}}}\right ) - \log \left (\log \left (x\right ) + 5\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (20) = 40\).
Time = 2.76 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.14 \[ \int \frac {25 x^2+e^x \left (-100 e^{4/x}+96 x^2\right )+\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)+\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{-25 x^2+e^x \left (25 e^{4/x} x^2+95 x^3\right )+\left (-10 x^2+e^x \left (10 e^{4/x} x^2+39 x^3\right )\right ) \log (x)+\left (-x^2+e^x \left (e^{4/x} x^2+4 x^3\right )\right ) \log ^2(x)} \, dx=- x + \log {\left (\frac {4 x \log {\left (x \right )} + 19 x}{\log {\left (x \right )} + 5} + e^{\frac {4}{x}} \right )} + \log {\left (\frac {- \log {\left (x \right )} - 5}{4 x \log {\left (x \right )} + 19 x + e^{\frac {4}{x}} \log {\left (x \right )} + 5 e^{\frac {4}{x}}} + e^{x} \right )} \]
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Time = 0.29 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.54 \[ \int \frac {25 x^2+e^x \left (-100 e^{4/x}+96 x^2\right )+\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)+\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{-25 x^2+e^x \left (25 e^{4/x} x^2+95 x^3\right )+\left (-10 x^2+e^x \left (10 e^{4/x} x^2+39 x^3\right )\right ) \log (x)+\left (-x^2+e^x \left (e^{4/x} x^2+4 x^3\right )\right ) \log ^2(x)} \, dx=\log \left (\frac {{\left ({\left (\log \left (x\right ) + 5\right )} e^{\left (x + \frac {4}{x}\right )} + {\left (4 \, x \log \left (x\right ) + 19 \, x\right )} e^{x} - \log \left (x\right ) - 5\right )} e^{\left (-x\right )}}{\log \left (x\right ) + 5}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 55 vs. \(2 (26) = 52\).
Time = 0.32 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.96 \[ \int \frac {25 x^2+e^x \left (-100 e^{4/x}+96 x^2\right )+\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)+\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{-25 x^2+e^x \left (25 e^{4/x} x^2+95 x^3\right )+\left (-10 x^2+e^x \left (10 e^{4/x} x^2+39 x^3\right )\right ) \log (x)+\left (-x^2+e^x \left (e^{4/x} x^2+4 x^3\right )\right ) \log ^2(x)} \, dx=-x + \log \left (4 \, x e^{x} \log \left (x\right ) + 19 \, x e^{x} + e^{\left (\frac {x^{2} + 4}{x}\right )} \log \left (x\right ) + 5 \, e^{\left (\frac {x^{2} + 4}{x}\right )} - \log \left (x\right ) - 5\right ) - \log \left (\log \left (x\right ) + 5\right ) \]
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Timed out. \[ \int \frac {25 x^2+e^x \left (-100 e^{4/x}+96 x^2\right )+\left (10 x^2+e^x \left (-40 e^{4/x}+39 x^2\right )\right ) \log (x)+\left (x^2+e^x \left (-4 e^{4/x}+4 x^2\right )\right ) \log ^2(x)}{-25 x^2+e^x \left (25 e^{4/x} x^2+95 x^3\right )+\left (-10 x^2+e^x \left (10 e^{4/x} x^2+39 x^3\right )\right ) \log (x)+\left (-x^2+e^x \left (e^{4/x} x^2+4 x^3\right )\right ) \log ^2(x)} \, dx=-\int \frac {{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^x\,\left (4\,{\mathrm {e}}^{4/x}-4\,x^2\right )-x^2\right )+\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (40\,{\mathrm {e}}^{4/x}-39\,x^2\right )-10\,x^2\right )+{\mathrm {e}}^x\,\left (100\,{\mathrm {e}}^{4/x}-96\,x^2\right )-25\,x^2}{\ln \left (x\right )\,\left ({\mathrm {e}}^x\,\left (10\,x^2\,{\mathrm {e}}^{4/x}+39\,x^3\right )-10\,x^2\right )+{\mathrm {e}}^x\,\left (25\,x^2\,{\mathrm {e}}^{4/x}+95\,x^3\right )-25\,x^2+{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^x\,\left (x^2\,{\mathrm {e}}^{4/x}+4\,x^3\right )-x^2\right )} \,d x \]
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