Integrand size = 466, antiderivative size = 35 \[ \int \frac {e^{5 x+x^2} \left (-512+2560 x+1024 x^2\right )+e^{5 x+x^2} \left (128 x-640 x^2-256 x^3\right ) \log \left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (-128 e^{5 x+x^2} x-512 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (-512 e^{5 x+x^2} x-2048 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^2\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (32 e^{5 x+x^2} x^2+128 x^3\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (128 e^{5 x+x^2} x^2+512 x^3\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )}{\left (\left (e^{5 x+x^2} x+4 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (4 e^{5 x+x^2} x+16 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )} \, dx=2+16 \left (-x+\frac {4}{\log \left (4+\frac {1}{\log \left (\frac {e^{x (5+x)}+4 x}{x}\right )}\right )}\right )^2 \]
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\[ \int \frac {e^{5 x+x^2} \left (-512+2560 x+1024 x^2\right )+e^{5 x+x^2} \left (128 x-640 x^2-256 x^3\right ) \log \left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (-128 e^{5 x+x^2} x-512 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (-512 e^{5 x+x^2} x-2048 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^2\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (32 e^{5 x+x^2} x^2+128 x^3\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (128 e^{5 x+x^2} x^2+512 x^3\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )}{\left (\left (e^{5 x+x^2} x+4 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (4 e^{5 x+x^2} x+16 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )} \, dx=\int \frac {e^{5 x+x^2} \left (-512+2560 x+1024 x^2\right )+e^{5 x+x^2} \left (128 x-640 x^2-256 x^3\right ) \log \left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (-128 e^{5 x+x^2} x-512 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (-512 e^{5 x+x^2} x-2048 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^2\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (32 e^{5 x+x^2} x^2+128 x^3\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (128 e^{5 x+x^2} x^2+512 x^3\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )}{\left (\left (e^{5 x+x^2} x+4 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (4 e^{5 x+x^2} x+16 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {32 \left (4-x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right ) \left (4 e^{x (5+x)} \left (-1+5 x+2 x^2\right )-x \left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )-4 x \left (e^{x (5+x)}+4 x\right ) \log ^2\left (4+\frac {e^{x (5+x)}}{x}\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{x \left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx \\ & = 32 \int \frac {\left (4-x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right ) \left (4 e^{x (5+x)} \left (-1+5 x+2 x^2\right )-x \left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )-4 x \left (e^{x (5+x)}+4 x\right ) \log ^2\left (4+\frac {e^{x (5+x)}}{x}\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{x \left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx \\ & = 32 \int \left (\frac {16 \left (-1+5 x+2 x^2\right ) \left (-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}-\frac {\left (-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right ) \left (-4+20 x+8 x^2-x \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )-4 x \log ^2\left (4+\frac {e^{x (5+x)}}{x}\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{x \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}\right ) \, dx \\ & = -\left (32 \int \frac {\left (-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right ) \left (-4+20 x+8 x^2-x \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )-4 x \log ^2\left (4+\frac {e^{x (5+x)}}{x}\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{x \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx\right )+512 \int \frac {\left (-1+5 x+2 x^2\right ) \left (-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx \\ & = -\left (32 \int \left (-x-\frac {16 \left (-1+5 x+2 x^2\right )}{x \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {4 \left (-1+5 x+2 x^2\right )}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {4}{\log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}\right ) \, dx\right )+512 \int \left (-\frac {-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {5 x \left (-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {2 x^2 \left (-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}\right ) \, dx \\ & = 16 x^2-128 \int \frac {-1+5 x+2 x^2}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx-128 \int \frac {1}{\log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx+512 \int \frac {-1+5 x+2 x^2}{x \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx-512 \int \frac {-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx+1024 \int \frac {x^2 \left (-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx+2560 \int \frac {x \left (-4+x \log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )\right )}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx \\ & = 16 x^2-128 \int \left (-\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {5 x}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {2 x^2}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}\right ) \, dx-128 \int \frac {1}{\log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx+512 \int \left (\frac {5}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}-\frac {1}{x \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {2 x}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}\right ) \, dx-512 \int \left (-\frac {4}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {x}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}\right ) \, dx+1024 \int \left (-\frac {4 x^2}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {x^3}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}\right ) \, dx+2560 \int \left (-\frac {4 x}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}+\frac {x^2}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )}\right ) \, dx \\ & = 16 x^2+128 \int \frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx-128 \int \frac {1}{\log \left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx-256 \int \frac {x^2}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx-512 \int \frac {1}{x \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx-512 \int \frac {x}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx-640 \int \frac {x}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx+1024 \int \frac {x}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx+1024 \int \frac {x^3}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx+2048 \int \frac {1}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx+2560 \int \frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx+2560 \int \frac {x^2}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx-4096 \int \frac {x^2}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx-10240 \int \frac {x}{\left (e^{x (5+x)}+4 x\right ) \log \left (4+\frac {e^{x (5+x)}}{x}\right ) \left (1+4 \log \left (4+\frac {e^{x (5+x)}}{x}\right )\right ) \log ^3\left (4+\frac {1}{\log \left (4+\frac {e^{x (5+x)}}{x}\right )}\right )} \, dx \\ \end{align*}
Time = 0.25 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.74 \[ \int \frac {e^{5 x+x^2} \left (-512+2560 x+1024 x^2\right )+e^{5 x+x^2} \left (128 x-640 x^2-256 x^3\right ) \log \left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (-128 e^{5 x+x^2} x-512 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (-512 e^{5 x+x^2} x-2048 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^2\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (32 e^{5 x+x^2} x^2+128 x^3\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (128 e^{5 x+x^2} x^2+512 x^3\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )}{\left (\left (e^{5 x+x^2} x+4 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (4 e^{5 x+x^2} x+16 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )} \, dx=32 \left (\frac {x^2}{2}+\frac {8}{\log ^2\left (4+\frac {1}{\log \left (4+\frac {e^{5 x+x^2}}{x}\right )}\right )}-\frac {4 x}{\log \left (4+\frac {1}{\log \left (4+\frac {e^{5 x+x^2}}{x}\right )}\right )}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(142\) vs. \(2(60)=120\).
Time = 2677.67 (sec) , antiderivative size = 143, normalized size of antiderivative = 4.09
method | result | size |
parallelrisch | \(-\frac {-16384-1024 {\ln \left (\frac {4 \ln \left (\frac {{\mathrm e}^{x^{2}+5 x}+4 x}{x}\right )+1}{\ln \left (\frac {{\mathrm e}^{x^{2}+5 x}+4 x}{x}\right )}\right )}^{2} x^{2}+8192 \ln \left (\frac {4 \ln \left (\frac {{\mathrm e}^{x^{2}+5 x}+4 x}{x}\right )+1}{\ln \left (\frac {{\mathrm e}^{x^{2}+5 x}+4 x}{x}\right )}\right ) x}{64 {\ln \left (\frac {4 \ln \left (\frac {{\mathrm e}^{x^{2}+5 x}+4 x}{x}\right )+1}{\ln \left (\frac {{\mathrm e}^{x^{2}+5 x}+4 x}{x}\right )}\right )}^{2}}\) | \(143\) |
risch | \(\text {Expression too large to display}\) | \(4421\) |
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Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (32) = 64\).
Time = 0.25 (sec) , antiderivative size = 141, normalized size of antiderivative = 4.03 \[ \int \frac {e^{5 x+x^2} \left (-512+2560 x+1024 x^2\right )+e^{5 x+x^2} \left (128 x-640 x^2-256 x^3\right ) \log \left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (-128 e^{5 x+x^2} x-512 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (-512 e^{5 x+x^2} x-2048 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^2\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (32 e^{5 x+x^2} x^2+128 x^3\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (128 e^{5 x+x^2} x^2+512 x^3\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )}{\left (\left (e^{5 x+x^2} x+4 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (4 e^{5 x+x^2} x+16 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )} \, dx=\frac {16 \, {\left (x^{2} \log \left (\frac {4 \, \log \left (\frac {4 \, x + e^{\left (x^{2} + 5 \, x\right )}}{x}\right ) + 1}{\log \left (\frac {4 \, x + e^{\left (x^{2} + 5 \, x\right )}}{x}\right )}\right )^{2} - 8 \, x \log \left (\frac {4 \, \log \left (\frac {4 \, x + e^{\left (x^{2} + 5 \, x\right )}}{x}\right ) + 1}{\log \left (\frac {4 \, x + e^{\left (x^{2} + 5 \, x\right )}}{x}\right )}\right ) + 16\right )}}{\log \left (\frac {4 \, \log \left (\frac {4 \, x + e^{\left (x^{2} + 5 \, x\right )}}{x}\right ) + 1}{\log \left (\frac {4 \, x + e^{\left (x^{2} + 5 \, x\right )}}{x}\right )}\right )^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (26) = 52\).
Time = 20.65 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.34 \[ \int \frac {e^{5 x+x^2} \left (-512+2560 x+1024 x^2\right )+e^{5 x+x^2} \left (128 x-640 x^2-256 x^3\right ) \log \left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (-128 e^{5 x+x^2} x-512 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (-512 e^{5 x+x^2} x-2048 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^2\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (32 e^{5 x+x^2} x^2+128 x^3\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (128 e^{5 x+x^2} x^2+512 x^3\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )}{\left (\left (e^{5 x+x^2} x+4 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (4 e^{5 x+x^2} x+16 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )} \, dx=16 x^{2} + \frac {- 128 x \log {\left (\frac {4 \log {\left (\frac {4 x + e^{x^{2} + 5 x}}{x} \right )} + 1}{\log {\left (\frac {4 x + e^{x^{2} + 5 x}}{x} \right )}} \right )} + 256}{\log {\left (\frac {4 \log {\left (\frac {4 x + e^{x^{2} + 5 x}}{x} \right )} + 1}{\log {\left (\frac {4 x + e^{x^{2} + 5 x}}{x} \right )}} \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 221 vs. \(2 (32) = 64\).
Time = 0.39 (sec) , antiderivative size = 221, normalized size of antiderivative = 6.31 \[ \int \frac {e^{5 x+x^2} \left (-512+2560 x+1024 x^2\right )+e^{5 x+x^2} \left (128 x-640 x^2-256 x^3\right ) \log \left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (-128 e^{5 x+x^2} x-512 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (-512 e^{5 x+x^2} x-2048 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^2\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (32 e^{5 x+x^2} x^2+128 x^3\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (128 e^{5 x+x^2} x^2+512 x^3\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )}{\left (\left (e^{5 x+x^2} x+4 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (4 e^{5 x+x^2} x+16 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )} \, dx=\frac {16 \, {\left (x^{2} \log \left (4 \, \log \left (4 \, x + e^{\left (x^{2} + 5 \, x\right )}\right ) - 4 \, \log \left (x\right ) + 1\right )^{2} + x^{2} \log \left (\log \left (4 \, x + e^{\left (x^{2} + 5 \, x\right )}\right ) - \log \left (x\right )\right )^{2} - 2 \, {\left (x^{2} \log \left (\log \left (4 \, x + e^{\left (x^{2} + 5 \, x\right )}\right ) - \log \left (x\right )\right ) + 4 \, x\right )} \log \left (4 \, \log \left (4 \, x + e^{\left (x^{2} + 5 \, x\right )}\right ) - 4 \, \log \left (x\right ) + 1\right ) + 8 \, x \log \left (\log \left (4 \, x + e^{\left (x^{2} + 5 \, x\right )}\right ) - \log \left (x\right )\right ) + 16\right )}}{\log \left (4 \, \log \left (4 \, x + e^{\left (x^{2} + 5 \, x\right )}\right ) - 4 \, \log \left (x\right ) + 1\right )^{2} - 2 \, \log \left (4 \, \log \left (4 \, x + e^{\left (x^{2} + 5 \, x\right )}\right ) - 4 \, \log \left (x\right ) + 1\right ) \log \left (\log \left (4 \, x + e^{\left (x^{2} + 5 \, x\right )}\right ) - \log \left (x\right )\right ) + \log \left (\log \left (4 \, x + e^{\left (x^{2} + 5 \, x\right )}\right ) - \log \left (x\right )\right )^{2}} \]
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Timed out. \[ \int \frac {e^{5 x+x^2} \left (-512+2560 x+1024 x^2\right )+e^{5 x+x^2} \left (128 x-640 x^2-256 x^3\right ) \log \left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (-128 e^{5 x+x^2} x-512 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (-512 e^{5 x+x^2} x-2048 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^2\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (32 e^{5 x+x^2} x^2+128 x^3\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (128 e^{5 x+x^2} x^2+512 x^3\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )}{\left (\left (e^{5 x+x^2} x+4 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (4 e^{5 x+x^2} x+16 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )} \, dx=\text {Timed out} \]
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Timed out. \[ \int \frac {e^{5 x+x^2} \left (-512+2560 x+1024 x^2\right )+e^{5 x+x^2} \left (128 x-640 x^2-256 x^3\right ) \log \left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (-128 e^{5 x+x^2} x-512 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (-512 e^{5 x+x^2} x-2048 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^2\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )+\left (\left (32 e^{5 x+x^2} x^2+128 x^3\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (128 e^{5 x+x^2} x^2+512 x^3\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )}{\left (\left (e^{5 x+x^2} x+4 x^2\right ) \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )+\left (4 e^{5 x+x^2} x+16 x^2\right ) \log ^2\left (\frac {e^{5 x+x^2}+4 x}{x}\right )\right ) \log ^3\left (\frac {1+4 \log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}{\log \left (\frac {e^{5 x+x^2}+4 x}{x}\right )}\right )} \, dx=\int -\frac {\left (\left (-128\,x^2\,{\mathrm {e}}^{x^2+5\,x}-512\,x^3\right )\,{\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )}^2+\left (-32\,x^2\,{\mathrm {e}}^{x^2+5\,x}-128\,x^3\right )\,\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )\right )\,{\ln \left (\frac {4\,\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )+1}{\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )}\right )}^3+\left (\left (512\,x\,{\mathrm {e}}^{x^2+5\,x}+2048\,x^2\right )\,{\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )}^2+\left (128\,x\,{\mathrm {e}}^{x^2+5\,x}+512\,x^2\right )\,\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )\right )\,{\ln \left (\frac {4\,\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )+1}{\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )}\right )}^2+{\mathrm {e}}^{x^2+5\,x}\,\left (256\,x^3+640\,x^2-128\,x\right )\,\ln \left (\frac {4\,\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )+1}{\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )}\right )-{\mathrm {e}}^{x^2+5\,x}\,\left (1024\,x^2+2560\,x-512\right )}{{\ln \left (\frac {4\,\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )+1}{\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )}\right )}^3\,\left (\left (4\,x\,{\mathrm {e}}^{x^2+5\,x}+16\,x^2\right )\,{\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )}^2+\left (x\,{\mathrm {e}}^{x^2+5\,x}+4\,x^2\right )\,\ln \left (\frac {4\,x+{\mathrm {e}}^{x^2+5\,x}}{x}\right )\right )} \,d x \]
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