Integrand size = 109, antiderivative size = 30 \[ \int \frac {5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )}{e^{32 x^2-8 x^3}+e^{16 x^2-4 x^3} (-8-2 x) \log \left (\frac {1}{x}\right )+\left (16+8 x+x^2\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=-3+\frac {5 x}{4+x-\frac {e^{4 (4-x) x^2}}{\log \left (\frac {1}{x}\right )}} \]
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\[ \int \frac {5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )}{e^{32 x^2-8 x^3}+e^{16 x^2-4 x^3} (-8-2 x) \log \left (\frac {1}{x}\right )+\left (16+8 x+x^2\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=\int \frac {5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )}{e^{32 x^2-8 x^3}+e^{16 x^2-4 x^3} (-8-2 x) \log \left (\frac {1}{x}\right )+\left (16+8 x+x^2\right ) \log ^2\left (\frac {1}{x}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{8 x^3} \left (5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )\right )}{\left (e^{16 x^2}-4 e^{4 x^3} \log \left (\frac {1}{x}\right )-e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2} \, dx \\ & = \int \left (-5 e^{8 x^3-4 x^2 (4+x)} \left (-1+\log \left (\frac {1}{x}\right )-32 x^2 \log \left (\frac {1}{x}\right )+12 x^3 \log \left (\frac {1}{x}\right )\right )+\frac {5 e^{8 x^3} (4+x) \log \left (\frac {1}{x}\right ) \left (-1+\log \left (\frac {1}{x}\right )-32 x^2 \log \left (\frac {1}{x}\right )+12 x^3 \log \left (\frac {1}{x}\right )\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}-\frac {5 e^{8 x^3} \log \left (\frac {1}{x}\right ) \left (-4-x+x \log \left (\frac {1}{x}\right )-128 x^2 \log \left (\frac {1}{x}\right )+16 x^3 \log \left (\frac {1}{x}\right )+12 x^4 \log \left (\frac {1}{x}\right )\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2}\right ) \, dx \\ & = -\left (5 \int e^{8 x^3-4 x^2 (4+x)} \left (-1+\log \left (\frac {1}{x}\right )-32 x^2 \log \left (\frac {1}{x}\right )+12 x^3 \log \left (\frac {1}{x}\right )\right ) \, dx\right )+5 \int \frac {e^{8 x^3} (4+x) \log \left (\frac {1}{x}\right ) \left (-1+\log \left (\frac {1}{x}\right )-32 x^2 \log \left (\frac {1}{x}\right )+12 x^3 \log \left (\frac {1}{x}\right )\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx-5 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right ) \left (-4-x+x \log \left (\frac {1}{x}\right )-128 x^2 \log \left (\frac {1}{x}\right )+16 x^3 \log \left (\frac {1}{x}\right )+12 x^4 \log \left (\frac {1}{x}\right )\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2} \, dx \\ & = \frac {5 e^{8 x^3-4 x^2 (4+x)} \left (8 x^2 \log \left (\frac {1}{x}\right )-3 x^3 \log \left (\frac {1}{x}\right )\right )}{5 x^2-2 x (4+x)}+5 \int \frac {e^{8 x^3} (4+x) \log \left (\frac {1}{x}\right ) \left (1-\left (1-32 x^2+12 x^3\right ) \log \left (\frac {1}{x}\right )\right )}{e^{32 x^2}-e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx-5 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right ) \left (-4-x+x \left (1-128 x+16 x^2+12 x^3\right ) \log \left (\frac {1}{x}\right )\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx \\ & = \frac {5 e^{8 x^3-4 x^2 (4+x)} \left (8 x^2 \log \left (\frac {1}{x}\right )-3 x^3 \log \left (\frac {1}{x}\right )\right )}{5 x^2-2 x (4+x)}-5 \int \left (-\frac {4 e^{8 x^3} \log \left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2}-\frac {e^{8 x^3} x \log \left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2}+\frac {e^{8 x^3} x \log ^2\left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2}-\frac {128 e^{8 x^3} x^2 \log ^2\left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2}+\frac {16 e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2}+\frac {12 e^{8 x^3} x^4 \log ^2\left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2}\right ) \, dx+5 \int \left (\frac {4 e^{8 x^3} \log \left (\frac {1}{x}\right ) \left (-1+\log \left (\frac {1}{x}\right )-32 x^2 \log \left (\frac {1}{x}\right )+12 x^3 \log \left (\frac {1}{x}\right )\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}+\frac {e^{8 x^3} x \log \left (\frac {1}{x}\right ) \left (-1+\log \left (\frac {1}{x}\right )-32 x^2 \log \left (\frac {1}{x}\right )+12 x^3 \log \left (\frac {1}{x}\right )\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}\right ) \, dx \\ & = \frac {5 e^{8 x^3-4 x^2 (4+x)} \left (8 x^2 \log \left (\frac {1}{x}\right )-3 x^3 \log \left (\frac {1}{x}\right )\right )}{5 x^2-2 x (4+x)}+5 \int \frac {e^{8 x^3} x \log \left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2} \, dx-5 \int \frac {e^{8 x^3} x \log ^2\left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2} \, dx+5 \int \frac {e^{8 x^3} x \log \left (\frac {1}{x}\right ) \left (-1+\log \left (\frac {1}{x}\right )-32 x^2 \log \left (\frac {1}{x}\right )+12 x^3 \log \left (\frac {1}{x}\right )\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx+20 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2} \, dx+20 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right ) \left (-1+\log \left (\frac {1}{x}\right )-32 x^2 \log \left (\frac {1}{x}\right )+12 x^3 \log \left (\frac {1}{x}\right )\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx-60 \int \frac {e^{8 x^3} x^4 \log ^2\left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2} \, dx-80 \int \frac {e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2} \, dx+640 \int \frac {e^{8 x^3} x^2 \log ^2\left (\frac {1}{x}\right )}{\left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )+e^{4 x^3} x \log \left (\frac {1}{x}\right )\right )^2} \, dx \\ & = \frac {5 e^{8 x^3-4 x^2 (4+x)} \left (8 x^2 \log \left (\frac {1}{x}\right )-3 x^3 \log \left (\frac {1}{x}\right )\right )}{5 x^2-2 x (4+x)}+5 \int \frac {e^{8 x^3} x \log \left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-5 \int \frac {e^{8 x^3} x \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx+5 \int \frac {e^{8 x^3} x \log \left (\frac {1}{x}\right ) \left (1-\left (1-32 x^2+12 x^3\right ) \log \left (\frac {1}{x}\right )\right )}{e^{32 x^2}-e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx+20 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx+20 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right ) \left (1-\left (1-32 x^2+12 x^3\right ) \log \left (\frac {1}{x}\right )\right )}{e^{32 x^2}-e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx-60 \int \frac {e^{8 x^3} x^4 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-80 \int \frac {e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx+640 \int \frac {e^{8 x^3} x^2 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx \\ & = \frac {5 e^{8 x^3-4 x^2 (4+x)} \left (8 x^2 \log \left (\frac {1}{x}\right )-3 x^3 \log \left (\frac {1}{x}\right )\right )}{5 x^2-2 x (4+x)}+5 \int \frac {e^{8 x^3} x \log \left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-5 \int \frac {e^{8 x^3} x \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx+5 \int \left (-\frac {e^{8 x^3} x \log \left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}+\frac {e^{8 x^3} x \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}-\frac {32 e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}+\frac {12 e^{8 x^3} x^4 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}\right ) \, dx+20 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx+20 \int \left (-\frac {e^{8 x^3} \log \left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}+\frac {e^{8 x^3} \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}-\frac {32 e^{8 x^3} x^2 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}+\frac {12 e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )}\right ) \, dx-60 \int \frac {e^{8 x^3} x^4 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-80 \int \frac {e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx+640 \int \frac {e^{8 x^3} x^2 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx \\ & = \frac {5 e^{8 x^3-4 x^2 (4+x)} \left (8 x^2 \log \left (\frac {1}{x}\right )-3 x^3 \log \left (\frac {1}{x}\right )\right )}{5 x^2-2 x (4+x)}-5 \int \frac {e^{8 x^3} x \log \left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx+5 \int \frac {e^{8 x^3} x \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx+5 \int \frac {e^{8 x^3} x \log \left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-5 \int \frac {e^{8 x^3} x \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-20 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx+20 \int \frac {e^{8 x^3} \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx+20 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx+60 \int \frac {e^{8 x^3} x^4 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx-60 \int \frac {e^{8 x^3} x^4 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-80 \int \frac {e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-160 \int \frac {e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx+240 \int \frac {e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx-640 \int \frac {e^{8 x^3} x^2 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+4 e^{4 x^2 (4+x)} \log \left (\frac {1}{x}\right )+e^{4 x^2 (4+x)} x \log \left (\frac {1}{x}\right )} \, dx+640 \int \frac {e^{8 x^3} x^2 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx \\ & = \frac {5 e^{8 x^3-4 x^2 (4+x)} \left (8 x^2 \log \left (\frac {1}{x}\right )-3 x^3 \log \left (\frac {1}{x}\right )\right )}{5 x^2-2 x (4+x)}+5 \int \frac {e^{8 x^3} x \log \left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-5 \int \frac {e^{8 x^3} x \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-5 \int \frac {e^{8 x^3} x \log \left (\frac {1}{x}\right )}{-e^{32 x^2}+e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx+5 \int \frac {e^{8 x^3} x \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx+20 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-20 \int \frac {e^{8 x^3} \log \left (\frac {1}{x}\right )}{-e^{32 x^2}+e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx+20 \int \frac {e^{8 x^3} \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx-60 \int \frac {e^{8 x^3} x^4 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx+60 \int \frac {e^{8 x^3} x^4 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx-80 \int \frac {e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-160 \int \frac {e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx+240 \int \frac {e^{8 x^3} x^3 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx+640 \int \frac {e^{8 x^3} x^2 \log ^2\left (\frac {1}{x}\right )}{\left (e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )\right )^2} \, dx-640 \int \frac {e^{8 x^3} x^2 \log ^2\left (\frac {1}{x}\right )}{-e^{32 x^2}+e^{4 x^2 (4+x)} (4+x) \log \left (\frac {1}{x}\right )} \, dx \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.70 \[ \int \frac {5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )}{e^{32 x^2-8 x^3}+e^{16 x^2-4 x^3} (-8-2 x) \log \left (\frac {1}{x}\right )+\left (16+8 x+x^2\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=\frac {5 \left (-e^{16 x^2}+4 e^{4 x^3} \log \left (\frac {1}{x}\right )\right )}{e^{16 x^2}-e^{4 x^3} (4+x) \log \left (\frac {1}{x}\right )} \]
[In]
[Out]
Time = 0.29 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23
method | result | size |
parallelrisch | \(\frac {5 x \ln \left (\frac {1}{x}\right )}{x \ln \left (\frac {1}{x}\right )+4 \ln \left (\frac {1}{x}\right )-{\mathrm e}^{-4 x^{3}+16 x^{2}}}\) | \(37\) |
risch | \(-\frac {20}{4+x}-\frac {5 x \,{\mathrm e}^{-4 \left (x -4\right ) x^{2}}}{\left (4+x \right ) \left (x \ln \left (x \right )+{\mathrm e}^{-4 \left (x -4\right ) x^{2}}+4 \ln \left (x \right )\right )}\) | \(46\) |
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Time = 0.39 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.53 \[ \int \frac {5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )}{e^{32 x^2-8 x^3}+e^{16 x^2-4 x^3} (-8-2 x) \log \left (\frac {1}{x}\right )+\left (16+8 x+x^2\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=\frac {5 \, {\left (e^{\left (-4 \, x^{3} + 16 \, x^{2}\right )} - 4 \, \log \left (\frac {1}{x}\right )\right )}}{{\left (x + 4\right )} \log \left (\frac {1}{x}\right ) - e^{\left (-4 \, x^{3} + 16 \, x^{2}\right )}} \]
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Time = 0.11 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.13 \[ \int \frac {5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )}{e^{32 x^2-8 x^3}+e^{16 x^2-4 x^3} (-8-2 x) \log \left (\frac {1}{x}\right )+\left (16+8 x+x^2\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=- \frac {5 x \log {\left (\frac {1}{x} \right )}}{- x \log {\left (\frac {1}{x} \right )} + e^{- 4 x^{3} + 16 x^{2}} - 4 \log {\left (\frac {1}{x} \right )}} \]
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Time = 0.27 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.33 \[ \int \frac {5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )}{e^{32 x^2-8 x^3}+e^{16 x^2-4 x^3} (-8-2 x) \log \left (\frac {1}{x}\right )+\left (16+8 x+x^2\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=-\frac {5 \, {\left (4 \, e^{\left (4 \, x^{3}\right )} \log \left (x\right ) + e^{\left (16 \, x^{2}\right )}\right )}}{{\left (x + 4\right )} e^{\left (4 \, x^{3}\right )} \log \left (x\right ) + e^{\left (16 \, x^{2}\right )}} \]
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Time = 0.38 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.93 \[ \int \frac {5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )}{e^{32 x^2-8 x^3}+e^{16 x^2-4 x^3} (-8-2 x) \log \left (\frac {1}{x}\right )+\left (16+8 x+x^2\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=\frac {5 \, x \log \left (x\right )}{x \log \left (x\right ) + e^{\left (-4 \, x^{3} + 16 \, x^{2}\right )} + 4 \, \log \left (x\right )} \]
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Timed out. \[ \int \frac {5 e^{16 x^2-4 x^3}+e^{16 x^2-4 x^3} \left (-5+160 x^2-60 x^3\right ) \log \left (\frac {1}{x}\right )+20 \log ^2\left (\frac {1}{x}\right )}{e^{32 x^2-8 x^3}+e^{16 x^2-4 x^3} (-8-2 x) \log \left (\frac {1}{x}\right )+\left (16+8 x+x^2\right ) \log ^2\left (\frac {1}{x}\right )} \, dx=\int \frac {20\,{\ln \left (\frac {1}{x}\right )}^2-{\mathrm {e}}^{16\,x^2-4\,x^3}\,\left (60\,x^3-160\,x^2+5\right )\,\ln \left (\frac {1}{x}\right )+5\,{\mathrm {e}}^{16\,x^2-4\,x^3}}{\left (x^2+8\,x+16\right )\,{\ln \left (\frac {1}{x}\right )}^2-{\mathrm {e}}^{16\,x^2-4\,x^3}\,\left (2\,x+8\right )\,\ln \left (\frac {1}{x}\right )+{\mathrm {e}}^{32\,x^2-8\,x^3}} \,d x \]
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