Integrand size = 54, antiderivative size = 24 \[ \int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{e^{2 e^{x^2}}-2 e^{e^{x^2}} x^3+x^6} \, dx=2 \left (4+e^5+\frac {x}{e^{e^{x^2}}-x^3}\right ) \]
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\[ \int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{e^{2 e^{x^2}}-2 e^{e^{x^2}} x^3+x^6} \, dx=\int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{e^{2 e^{x^2}}-2 e^{e^{x^2}} x^3+x^6} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{\left (e^{e^{x^2}}-x^3\right )^2} \, dx \\ & = \int \left (-\frac {4 e^{e^{x^2}+x^2} x^2}{\left (e^{e^{x^2}}-x^3\right )^2}+\frac {2 \left (e^{e^{x^2}}+2 x^3\right )}{\left (e^{e^{x^2}}-x^3\right )^2}\right ) \, dx \\ & = 2 \int \frac {e^{e^{x^2}}+2 x^3}{\left (e^{e^{x^2}}-x^3\right )^2} \, dx-4 \int \frac {e^{e^{x^2}+x^2} x^2}{\left (e^{e^{x^2}}-x^3\right )^2} \, dx \\ & = 2 \int \left (\frac {1}{e^{e^{x^2}}-x^3}+\frac {3 x^3}{\left (-e^{e^{x^2}}+x^3\right )^2}\right ) \, dx-4 \int \frac {e^{e^{x^2}+x^2} x^2}{\left (e^{e^{x^2}}-x^3\right )^2} \, dx \\ & = 2 \int \frac {1}{e^{e^{x^2}}-x^3} \, dx-4 \int \frac {e^{e^{x^2}+x^2} x^2}{\left (e^{e^{x^2}}-x^3\right )^2} \, dx+6 \int \frac {x^3}{\left (-e^{e^{x^2}}+x^3\right )^2} \, dx \\ \end{align*}
Time = 0.37 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.75 \[ \int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{e^{2 e^{x^2}}-2 e^{e^{x^2}} x^3+x^6} \, dx=\frac {2 x}{e^{e^{x^2}}-x^3} \]
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Time = 0.10 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71
method | result | size |
risch | \(-\frac {2 x}{x^{3}-{\mathrm e}^{{\mathrm e}^{x^{2}}}}\) | \(17\) |
parallelrisch | \(-\frac {2 x}{x^{3}-{\mathrm e}^{{\mathrm e}^{x^{2}}}}\) | \(17\) |
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Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{e^{2 e^{x^2}}-2 e^{e^{x^2}} x^3+x^6} \, dx=-\frac {2 \, x}{x^{3} - e^{\left (e^{\left (x^{2}\right )}\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.50 \[ \int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{e^{2 e^{x^2}}-2 e^{e^{x^2}} x^3+x^6} \, dx=\frac {2 x}{- x^{3} + e^{e^{x^{2}}}} \]
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Time = 0.22 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{e^{2 e^{x^2}}-2 e^{e^{x^2}} x^3+x^6} \, dx=-\frac {2 \, x}{x^{3} - e^{\left (e^{\left (x^{2}\right )}\right )}} \]
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Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{e^{2 e^{x^2}}-2 e^{e^{x^2}} x^3+x^6} \, dx=-\frac {2 \, x}{x^{3} - e^{\left (e^{\left (x^{2}\right )}\right )}} \]
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Time = 13.14 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \frac {4 x^3+e^{e^{x^2}} \left (2-4 e^{x^2} x^2\right )}{e^{2 e^{x^2}}-2 e^{e^{x^2}} x^3+x^6} \, dx=\frac {2\,x}{{\mathrm {e}}^{{\mathrm {e}}^{x^2}}-x^3} \]
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