Integrand size = 151, antiderivative size = 30 \[ \int \frac {e^{\frac {-3-4 x+\log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )}{x}} \left (3 x-4 x^2+6 x^4+\left (4-8 x^2\right ) \log \left (x^2\right )+2 \log ^2\left (x^2\right )+\left (-x-x^4+2 x^2 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )\right )}{x^3+x^6-2 x^4 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )} \, dx=e^{-5+\frac {-3+x+\log \left (\frac {x+\left (-x^2+\log \left (x^2\right )\right )^2}{x}\right )}{x}} \]
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Time = 0.92 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.37, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.007, Rules used = {6838} \[ \int \frac {e^{\frac {-3-4 x+\log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )}{x}} \left (3 x-4 x^2+6 x^4+\left (4-8 x^2\right ) \log \left (x^2\right )+2 \log ^2\left (x^2\right )+\left (-x-x^4+2 x^2 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )\right )}{x^3+x^6-2 x^4 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )} \, dx=e^{-\frac {4 x+3}{x}} \left (\frac {x^4+\log ^2\left (x^2\right )-2 x^2 \log \left (x^2\right )+x}{x}\right )^{\frac {1}{x}} \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = e^{-\frac {3+4 x}{x}} \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )^{\frac {1}{x}} \\ \end{align*}
Time = 0.18 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.20 \[ \int \frac {e^{\frac {-3-4 x+\log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )}{x}} \left (3 x-4 x^2+6 x^4+\left (4-8 x^2\right ) \log \left (x^2\right )+2 \log ^2\left (x^2\right )+\left (-x-x^4+2 x^2 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )\right )}{x^3+x^6-2 x^4 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )} \, dx=e^{-4-\frac {3}{x}} \left (1+x^3-2 x \log \left (x^2\right )+\frac {\log ^2\left (x^2\right )}{x}\right )^{\frac {1}{x}} \]
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Time = 16.21 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.20
method | result | size |
parallelrisch | \({\mathrm e}^{\frac {\ln \left (\frac {\ln \left (x^{2}\right )^{2}-2 x^{2} \ln \left (x^{2}\right )+x^{4}+x}{x}\right )-4 x -3}{x}}\) | \(36\) |
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Time = 0.26 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.27 \[ \int \frac {e^{\frac {-3-4 x+\log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )}{x}} \left (3 x-4 x^2+6 x^4+\left (4-8 x^2\right ) \log \left (x^2\right )+2 \log ^2\left (x^2\right )+\left (-x-x^4+2 x^2 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )\right )}{x^3+x^6-2 x^4 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )} \, dx=e^{\left (-\frac {4 \, x - \log \left (\frac {x^{4} - 2 \, x^{2} \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + x}{x}\right ) + 3}{x}\right )} \]
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Time = 1.53 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {e^{\frac {-3-4 x+\log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )}{x}} \left (3 x-4 x^2+6 x^4+\left (4-8 x^2\right ) \log \left (x^2\right )+2 \log ^2\left (x^2\right )+\left (-x-x^4+2 x^2 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )\right )}{x^3+x^6-2 x^4 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )} \, dx=e^{\frac {- 4 x + \log {\left (\frac {x^{4} - 2 x^{2} \log {\left (x^{2} \right )} + x + \log {\left (x^{2} \right )}^{2}}{x} \right )} - 3}{x}} \]
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Time = 0.29 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.27 \[ \int \frac {e^{\frac {-3-4 x+\log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )}{x}} \left (3 x-4 x^2+6 x^4+\left (4-8 x^2\right ) \log \left (x^2\right )+2 \log ^2\left (x^2\right )+\left (-x-x^4+2 x^2 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )\right )}{x^3+x^6-2 x^4 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )} \, dx=e^{\left (\frac {\log \left (x^{4} - 4 \, x^{2} \log \left (x\right ) + 4 \, \log \left (x\right )^{2} + x\right )}{x} - \frac {\log \left (x\right )}{x} - \frac {3}{x} - 4\right )} \]
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Time = 0.69 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.17 \[ \int \frac {e^{\frac {-3-4 x+\log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )}{x}} \left (3 x-4 x^2+6 x^4+\left (4-8 x^2\right ) \log \left (x^2\right )+2 \log ^2\left (x^2\right )+\left (-x-x^4+2 x^2 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )\right )}{x^3+x^6-2 x^4 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )} \, dx=e^{\left (\frac {\log \left (x^{3} - 2 \, x \log \left (x^{2}\right ) + \frac {\log \left (x^{2}\right )^{2}}{x} + 1\right )}{x} - \frac {3}{x} - 4\right )} \]
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Time = 14.50 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.17 \[ \int \frac {e^{\frac {-3-4 x+\log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )}{x}} \left (3 x-4 x^2+6 x^4+\left (4-8 x^2\right ) \log \left (x^2\right )+2 \log ^2\left (x^2\right )+\left (-x-x^4+2 x^2 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \log \left (\frac {x+x^4-2 x^2 \log \left (x^2\right )+\log ^2\left (x^2\right )}{x}\right )\right )}{x^3+x^6-2 x^4 \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )} \, dx={\mathrm {e}}^{-4}\,{\mathrm {e}}^{-\frac {3}{x}}\,{\left (x^3-2\,x\,\ln \left (x^2\right )+\frac {{\ln \left (x^2\right )}^2}{x}+1\right )}^{1/x} \]
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