Integrand size = 191, antiderivative size = 26 \[ \int \frac {4-10 x+4 x^2+e^x \left (-1-2 x+7 x^2-4 x^3\right )+\left (-8+9 x+e^x \left (2+5 x-6 x^2-x^3\right )\right ) \log (x)+\left (4+e^x \left (-1-2 x-2 x^2\right )\right ) \log ^2(x)-e^x x \log ^3(x)}{x^2-x^3+e^x \left (4 x-8 x^2+4 x^3\right )+\left (-4 x+7 x^2-4 x^3+e^x \left (-7 x+6 x^2+x^3\right )\right ) \log (x)+\left (8 x-8 x^2+e^x \left (2 x+2 x^2\right )\right ) \log ^2(x)+\left (-4 x+e^x x\right ) \log ^3(x)} \, dx=\log \left (\frac {1}{-4 \log (x)+e^x (4+\log (x))-\frac {x}{-1+x+\log (x)}}\right ) \]
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\[ \int \frac {4-10 x+4 x^2+e^x \left (-1-2 x+7 x^2-4 x^3\right )+\left (-8+9 x+e^x \left (2+5 x-6 x^2-x^3\right )\right ) \log (x)+\left (4+e^x \left (-1-2 x-2 x^2\right )\right ) \log ^2(x)-e^x x \log ^3(x)}{x^2-x^3+e^x \left (4 x-8 x^2+4 x^3\right )+\left (-4 x+7 x^2-4 x^3+e^x \left (-7 x+6 x^2+x^3\right )\right ) \log (x)+\left (8 x-8 x^2+e^x \left (2 x+2 x^2\right )\right ) \log ^2(x)+\left (-4 x+e^x x\right ) \log ^3(x)} \, dx=\int \frac {4-10 x+4 x^2+e^x \left (-1-2 x+7 x^2-4 x^3\right )+\left (-8+9 x+e^x \left (2+5 x-6 x^2-x^3\right )\right ) \log (x)+\left (4+e^x \left (-1-2 x-2 x^2\right )\right ) \log ^2(x)-e^x x \log ^3(x)}{x^2-x^3+e^x \left (4 x-8 x^2+4 x^3\right )+\left (-4 x+7 x^2-4 x^3+e^x \left (-7 x+6 x^2+x^3\right )\right ) \log (x)+\left (8 x-8 x^2+e^x \left (2 x+2 x^2\right )\right ) \log ^2(x)+\left (-4 x+e^x x\right ) \log ^3(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-4+10 x-4 x^2+e^x (-1+x)^2 (1+4 x)+\left (8-9 x+e^x \left (-2-5 x+6 x^2+x^3\right )\right ) \log (x)+\left (-4+e^x \left (1+2 x+2 x^2\right )\right ) \log ^2(x)+e^x x \log ^3(x)}{x (1-x-\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx \\ & = \int \left (\frac {-1-4 x-x \log (x)}{x (4+\log (x))}-\frac {-16+39 x-19 x^2+4 x^3+32 \log (x)-17 x \log (x)-29 x^2 \log (x)+17 x^3 \log (x)-16 \log ^2(x)-29 x \log ^2(x)+25 x^2 \log ^2(x)+4 x^3 \log ^2(x)+8 x \log ^3(x)+8 x^2 \log ^3(x)+4 x \log ^4(x)}{x (4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}\right ) \, dx \\ & = \int \frac {-1-4 x-x \log (x)}{x (4+\log (x))} \, dx-\int \frac {-16+39 x-19 x^2+4 x^3+32 \log (x)-17 x \log (x)-29 x^2 \log (x)+17 x^3 \log (x)-16 \log ^2(x)-29 x \log ^2(x)+25 x^2 \log ^2(x)+4 x^3 \log ^2(x)+8 x \log ^3(x)+8 x^2 \log ^3(x)+4 x \log ^4(x)}{x (4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx \\ & = \int \left (-1-\frac {1}{x (4+\log (x))}\right ) \, dx-\int \left (\frac {39}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}-\frac {16}{x (4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}-\frac {19 x}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}+\frac {4 x^2}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}-\frac {17 \log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}+\frac {32 \log (x)}{x (4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}-\frac {29 x \log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}+\frac {17 x^2 \log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}-\frac {29 \log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}-\frac {16 \log ^2(x)}{x (4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}+\frac {25 x \log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}+\frac {4 x^2 \log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}+\frac {8 \log ^3(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}+\frac {8 x \log ^3(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}+\frac {4 \log ^4(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )}\right ) \, dx \\ & = -x-4 \int \frac {x^2}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx-4 \int \frac {x^2 \log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx-4 \int \frac {\log ^4(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx-8 \int \frac {\log ^3(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx-8 \int \frac {x \log ^3(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx+16 \int \frac {1}{x (4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx+16 \int \frac {\log ^2(x)}{x (4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx+17 \int \frac {\log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx-17 \int \frac {x^2 \log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx+19 \int \frac {x}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx-25 \int \frac {x \log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx+29 \int \frac {x \log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx+29 \int \frac {\log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx-32 \int \frac {\log (x)}{x (4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx-39 \int \frac {1}{(4+\log (x)) (-1+x+\log (x)) \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right )} \, dx-\int \frac {1}{x (4+\log (x))} \, dx \\ & = -x-4 \int \frac {x^2}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-4 \int \frac {x^2 \log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-4 \int \frac {\log ^4(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-8 \int \frac {\log ^3(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-8 \int \frac {x \log ^3(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+16 \int \frac {1}{x (4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+16 \int \frac {\log ^2(x)}{x (4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+17 \int \frac {\log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-17 \int \frac {x^2 \log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+19 \int \frac {x}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-25 \int \frac {x \log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+29 \int \frac {x \log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+29 \int \frac {\log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-32 \int \frac {\log (x)}{x (4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-39 \int \frac {1}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-\text {Subst}\left (\int \frac {1}{x} \, dx,x,4+\log (x)\right ) \\ & = -x-\log (4+\log (x))-4 \int \frac {x^2}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-4 \int \frac {x^2 \log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-4 \int \frac {\log ^4(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-8 \int \frac {\log ^3(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-8 \int \frac {x \log ^3(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+16 \int \frac {1}{x (4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+16 \int \frac {\log ^2(x)}{x (4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+17 \int \frac {\log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-17 \int \frac {x^2 \log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+19 \int \frac {x}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-25 \int \frac {x \log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+29 \int \frac {x \log (x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx+29 \int \frac {\log ^2(x)}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-32 \int \frac {\log (x)}{x (4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx-39 \int \frac {1}{(4+\log (x)) (-1+x+\log (x)) \left (4 e^x (-1+x)-x+\left (4-4 x+e^x (3+x)\right ) \log (x)+\left (-4+e^x\right ) \log ^2(x)\right )} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(66\) vs. \(2(26)=52\).
Time = 0.22 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.54 \[ \int \frac {4-10 x+4 x^2+e^x \left (-1-2 x+7 x^2-4 x^3\right )+\left (-8+9 x+e^x \left (2+5 x-6 x^2-x^3\right )\right ) \log (x)+\left (4+e^x \left (-1-2 x-2 x^2\right )\right ) \log ^2(x)-e^x x \log ^3(x)}{x^2-x^3+e^x \left (4 x-8 x^2+4 x^3\right )+\left (-4 x+7 x^2-4 x^3+e^x \left (-7 x+6 x^2+x^3\right )\right ) \log (x)+\left (8 x-8 x^2+e^x \left (2 x+2 x^2\right )\right ) \log ^2(x)+\left (-4 x+e^x x\right ) \log ^3(x)} \, dx=\log (1-x-\log (x))-\log \left (-4 e^x-x+4 e^x x+4 \log (x)+3 e^x \log (x)-4 x \log (x)+e^x x \log (x)-4 \log ^2(x)+e^x \log ^2(x)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs. \(2(25)=50\).
Time = 0.42 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.23
method | result | size |
parallelrisch | \(\ln \left (-1+\ln \left (x \right )+x \right )-\ln \left ({\mathrm e}^{x} \ln \left (x \right )^{2}+x \,{\mathrm e}^{x} \ln \left (x \right )+3 \,{\mathrm e}^{x} \ln \left (x \right )+4 \,{\mathrm e}^{x} x -4 \ln \left (x \right )^{2}-4 x \ln \left (x \right )-4 \,{\mathrm e}^{x}+4 \ln \left (x \right )-x \right )\) | \(58\) |
risch | \(-\ln \left ({\mathrm e}^{x}-4\right )+\ln \left (-1+\ln \left (x \right )+x \right )-\ln \left (\ln \left (x \right )^{2}+\frac {\left ({\mathrm e}^{x} x -4 x +3 \,{\mathrm e}^{x}+4\right ) \ln \left (x \right )}{{\mathrm e}^{x}-4}+\frac {4 \,{\mathrm e}^{x} x -x -4 \,{\mathrm e}^{x}}{{\mathrm e}^{x}-4}\right )\) | \(65\) |
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Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (25) = 50\).
Time = 0.28 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.23 \[ \int \frac {4-10 x+4 x^2+e^x \left (-1-2 x+7 x^2-4 x^3\right )+\left (-8+9 x+e^x \left (2+5 x-6 x^2-x^3\right )\right ) \log (x)+\left (4+e^x \left (-1-2 x-2 x^2\right )\right ) \log ^2(x)-e^x x \log ^3(x)}{x^2-x^3+e^x \left (4 x-8 x^2+4 x^3\right )+\left (-4 x+7 x^2-4 x^3+e^x \left (-7 x+6 x^2+x^3\right )\right ) \log (x)+\left (8 x-8 x^2+e^x \left (2 x+2 x^2\right )\right ) \log ^2(x)+\left (-4 x+e^x x\right ) \log ^3(x)} \, dx=\log \left (x + \log \left (x\right ) - 1\right ) - \log \left (\frac {{\left (e^{x} - 4\right )} \log \left (x\right )^{2} + 4 \, {\left (x - 1\right )} e^{x} + {\left ({\left (x + 3\right )} e^{x} - 4 \, x + 4\right )} \log \left (x\right ) - x}{e^{x} - 4}\right ) - \log \left (e^{x} - 4\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (24) = 48\).
Time = 1.55 (sec) , antiderivative size = 53, normalized size of antiderivative = 2.04 \[ \int \frac {4-10 x+4 x^2+e^x \left (-1-2 x+7 x^2-4 x^3\right )+\left (-8+9 x+e^x \left (2+5 x-6 x^2-x^3\right )\right ) \log (x)+\left (4+e^x \left (-1-2 x-2 x^2\right )\right ) \log ^2(x)-e^x x \log ^3(x)}{x^2-x^3+e^x \left (4 x-8 x^2+4 x^3\right )+\left (-4 x+7 x^2-4 x^3+e^x \left (-7 x+6 x^2+x^3\right )\right ) \log (x)+\left (8 x-8 x^2+e^x \left (2 x+2 x^2\right )\right ) \log ^2(x)+\left (-4 x+e^x x\right ) \log ^3(x)} \, dx=- \log {\left (\frac {- 4 x \log {\left (x \right )} - x - 4 \log {\left (x \right )}^{2} + 4 \log {\left (x \right )}}{x \log {\left (x \right )} + 4 x + \log {\left (x \right )}^{2} + 3 \log {\left (x \right )} - 4} + e^{x} \right )} - \log {\left (\log {\left (x \right )} + 4 \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (25) = 50\).
Time = 0.30 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.46 \[ \int \frac {4-10 x+4 x^2+e^x \left (-1-2 x+7 x^2-4 x^3\right )+\left (-8+9 x+e^x \left (2+5 x-6 x^2-x^3\right )\right ) \log (x)+\left (4+e^x \left (-1-2 x-2 x^2\right )\right ) \log ^2(x)-e^x x \log ^3(x)}{x^2-x^3+e^x \left (4 x-8 x^2+4 x^3\right )+\left (-4 x+7 x^2-4 x^3+e^x \left (-7 x+6 x^2+x^3\right )\right ) \log (x)+\left (8 x-8 x^2+e^x \left (2 x+2 x^2\right )\right ) \log ^2(x)+\left (-4 x+e^x x\right ) \log ^3(x)} \, dx=-\log \left (\frac {{\left ({\left (x + 3\right )} \log \left (x\right ) + \log \left (x\right )^{2} + 4 \, x - 4\right )} e^{x} - 4 \, {\left (x - 1\right )} \log \left (x\right ) - 4 \, \log \left (x\right )^{2} - x}{{\left (x + 3\right )} \log \left (x\right ) + \log \left (x\right )^{2} + 4 \, x - 4}\right ) - \log \left (\log \left (x\right ) + 4\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (25) = 50\).
Time = 0.50 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.19 \[ \int \frac {4-10 x+4 x^2+e^x \left (-1-2 x+7 x^2-4 x^3\right )+\left (-8+9 x+e^x \left (2+5 x-6 x^2-x^3\right )\right ) \log (x)+\left (4+e^x \left (-1-2 x-2 x^2\right )\right ) \log ^2(x)-e^x x \log ^3(x)}{x^2-x^3+e^x \left (4 x-8 x^2+4 x^3\right )+\left (-4 x+7 x^2-4 x^3+e^x \left (-7 x+6 x^2+x^3\right )\right ) \log (x)+\left (8 x-8 x^2+e^x \left (2 x+2 x^2\right )\right ) \log ^2(x)+\left (-4 x+e^x x\right ) \log ^3(x)} \, dx=-\log \left (x e^{x} \log \left (x\right ) + e^{x} \log \left (x\right )^{2} + 4 \, x e^{x} - 4 \, x \log \left (x\right ) + 3 \, e^{x} \log \left (x\right ) - 4 \, \log \left (x\right )^{2} - x - 4 \, e^{x} + 4 \, \log \left (x\right )\right ) + \log \left (x + \log \left (x\right ) - 1\right ) \]
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Timed out. \[ \int \frac {4-10 x+4 x^2+e^x \left (-1-2 x+7 x^2-4 x^3\right )+\left (-8+9 x+e^x \left (2+5 x-6 x^2-x^3\right )\right ) \log (x)+\left (4+e^x \left (-1-2 x-2 x^2\right )\right ) \log ^2(x)-e^x x \log ^3(x)}{x^2-x^3+e^x \left (4 x-8 x^2+4 x^3\right )+\left (-4 x+7 x^2-4 x^3+e^x \left (-7 x+6 x^2+x^3\right )\right ) \log (x)+\left (8 x-8 x^2+e^x \left (2 x+2 x^2\right )\right ) \log ^2(x)+\left (-4 x+e^x x\right ) \log ^3(x)} \, dx=\int \frac {10\,x-\ln \left (x\right )\,\left (9\,x+{\mathrm {e}}^x\,\left (-x^3-6\,x^2+5\,x+2\right )-8\right )+{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^x\,\left (2\,x^2+2\,x+1\right )-4\right )-4\,x^2+{\mathrm {e}}^x\,\left (4\,x^3-7\,x^2+2\,x+1\right )+x\,{\mathrm {e}}^x\,{\ln \left (x\right )}^3-4}{\ln \left (x\right )\,\left (4\,x-{\mathrm {e}}^x\,\left (x^3+6\,x^2-7\,x\right )-7\,x^2+4\,x^3\right )+{\ln \left (x\right )}^3\,\left (4\,x-x\,{\mathrm {e}}^x\right )-{\ln \left (x\right )}^2\,\left (8\,x+{\mathrm {e}}^x\,\left (2\,x^2+2\,x\right )-8\,x^2\right )-x^2+x^3-{\mathrm {e}}^x\,\left (4\,x^3-8\,x^2+4\,x\right )} \,d x \]
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