Optimal. Leaf size=30 \[ -3+\frac {2}{-e^{3+x-x^2 (-2+x (-x+\log (x)))}+x} \]
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Rubi [F] time = 2.44, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-2+e^{3+x+2 x^2+x^4-x^3 \log (x)} \left (2+8 x-2 x^2+8 x^3-6 x^2 \log (x)\right )}{e^{6+2 x+4 x^2+2 x^4-2 x^3 \log (x)}-2 e^{3+x+2 x^2+x^4-x^3 \log (x)} x+x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^{2 x^3} \left (-2+e^{3+x+2 x^2+x^4-x^3 \log (x)} \left (2+8 x-2 x^2+8 x^3-6 x^2 \log (x)\right )\right )}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx\\ &=\int \left (\frac {2 e^{3+x+2 x^2+x^4} x^{x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2}-\frac {2 x^{2 x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2}+\frac {8 e^{3+x+2 x^2+x^4} x^{1+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2}-\frac {2 e^{3+x+2 x^2+x^4} x^{2+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2}+\frac {8 e^{3+x+2 x^2+x^4} x^{3+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2}-\frac {6 e^{3+x+2 x^2+x^4} x^{2+x^3} \log (x)}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2}\right ) \, dx\\ &=2 \int \frac {e^{3+x+2 x^2+x^4} x^{x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx-2 \int \frac {x^{2 x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx-2 \int \frac {e^{3+x+2 x^2+x^4} x^{2+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx-6 \int \frac {e^{3+x+2 x^2+x^4} x^{2+x^3} \log (x)}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx+8 \int \frac {e^{3+x+2 x^2+x^4} x^{1+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx+8 \int \frac {e^{3+x+2 x^2+x^4} x^{3+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx\\ &=2 \int \frac {e^{3+x+2 x^2+x^4} x^{x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx-2 \int \frac {x^{2 x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx-2 \int \frac {e^{3+x+2 x^2+x^4} x^{2+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx+6 \int \frac {\int \frac {e^{3+x+2 x^2+x^4} x^{2+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx}{x} \, dx+8 \int \frac {e^{3+x+2 x^2+x^4} x^{1+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx+8 \int \frac {e^{3+x+2 x^2+x^4} x^{3+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx-(6 \log (x)) \int \frac {e^{3+x+2 x^2+x^4} x^{2+x^3}}{\left (e^{3+x+2 x^2+x^4}-x^{1+x^3}\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 32, normalized size = 1.07 \begin {gather*} -\frac {2 x^{x^3}}{e^{3+x+2 x^2+x^4}-x^{1+x^3}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.94, size = 27, normalized size = 0.90 \begin {gather*} \frac {2}{x - e^{\left (x^{4} - x^{3} \log \relax (x) + 2 \, x^{2} + x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 3.98, size = 27, normalized size = 0.90 \begin {gather*} \frac {2}{x - e^{\left (x^{4} - x^{3} \log \relax (x) + 2 \, x^{2} + x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 28, normalized size = 0.93
method | result | size |
risch | \(\frac {2}{x -x^{-x^{3}} {\mathrm e}^{x^{4}+2 x^{2}+x +3}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 31, normalized size = 1.03 \begin {gather*} \frac {2 \, x^{\left (x^{3}\right )}}{x x^{\left (x^{3}\right )} - e^{\left (x^{4} + 2 \, x^{2} + x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.43, size = 29, normalized size = 0.97 \begin {gather*} \frac {2}{x-\frac {{\mathrm {e}}^{x^4}\,{\mathrm {e}}^3\,{\mathrm {e}}^{2\,x^2}\,{\mathrm {e}}^x}{x^{x^3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 24, normalized size = 0.80 \begin {gather*} - \frac {2}{- x + e^{x^{4} - x^{3} \log {\relax (x )} + 2 x^{2} + x + 3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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