Optimal. Leaf size=47 \[ \frac {e^{-2 a}}{1-e^{2 a} x^4}+e^{-2 a} \log \left (1-e^{2 a} x^4\right )+\frac {x^4}{4} \]
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Rubi [F] time = 0.07, 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 = {} \[ \int x^3 \coth ^2(a+2 \log (x)) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int x^3 \coth ^2(a+2 \log (x)) \, dx &=\int x^3 \coth ^2(a+2 \log (x)) \, dx\\ \end {align*}
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Mathematica [A] time = 0.11, size = 86, normalized size = 1.83 \[ \frac {\sinh (3 a)-\cosh (3 a)}{\left (x^4+1\right ) \sinh (a)+\left (x^4-1\right ) \cosh (a)}+\cosh (2 a) \log \left (\left (x^4+1\right ) \sinh (a)+\left (x^4-1\right ) \cosh (a)\right )-\sinh (2 a) \log \left (\left (x^4+1\right ) \sinh (a)+\left (x^4-1\right ) \cosh (a)\right )+\frac {x^4}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 61, normalized size = 1.30 \[ \frac {x^{8} e^{\left (4 \, a\right )} - x^{4} e^{\left (2 \, a\right )} + 4 \, {\left (x^{4} e^{\left (2 \, a\right )} - 1\right )} \log \left (x^{4} e^{\left (2 \, a\right )} - 1\right ) - 4}{4 \, {\left (x^{4} e^{\left (4 \, a\right )} - e^{\left (2 \, a\right )}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.11, size = 40, normalized size = 0.85 \[ \frac {1}{4} \, x^{4} - \frac {x^{4}}{x^{4} e^{\left (2 \, a\right )} - 1} + e^{\left (-2 \, a\right )} \log \left ({\left | x^{4} e^{\left (2 \, a\right )} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 41, normalized size = 0.87 \[ \frac {x^{4}}{4}-\frac {{\mathrm e}^{-2 a}}{-1+{\mathrm e}^{2 a} x^{4}}+{\mathrm e}^{-2 a} \ln \left (-1+{\mathrm e}^{2 a} x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 53, normalized size = 1.13 \[ \frac {1}{4} \, x^{4} + e^{\left (-2 \, a\right )} \log \left (x^{2} e^{a} + 1\right ) + e^{\left (-2 \, a\right )} \log \left (x^{2} e^{a} - 1\right ) - \frac {1}{x^{4} e^{\left (4 \, a\right )} - e^{\left (2 \, a\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.25, size = 40, normalized size = 0.85 \[ \ln \left (x^4-{\mathrm {e}}^{-2\,a}\right )\,{\mathrm {e}}^{-2\,a}-\frac {{\mathrm {e}}^{-2\,a}}{x^4\,{\mathrm {e}}^{2\,a}-1}+\frac {x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{3} \coth ^{2}{\left (a + 2 \log {\relax (x )} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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