Optimal. Leaf size=47 \[ -\frac {e^{-2 a}}{e^{2 a} x^4+1}-e^{-2 a} \log \left (e^{2 a} x^4+1\right )+\frac {x^4}{4} \]
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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 = {} \[ \int x^3 \tanh ^2(a+2 \log (x)) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int x^3 \tanh ^2(a+2 \log (x)) \, dx &=\int x^3 \tanh ^2(a+2 \log (x)) \, dx\\ \end {align*}
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Mathematica [A] time = 0.12, 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 = 0.51, size = 58, normalized size = 1.23 \[ \frac {x^{8} e^{\left (4 \, a\right )} + x^{4} e^{\left (2 \, a\right )} - 4 \, {\left (x^{4} e^{\left (2 \, a\right )} + 1\right )} \log \left (x^{4} e^{\left (2 \, a\right )} + 1\right ) - 4}{4 \, {\left (x^{4} e^{\left (4 \, a\right )} + e^{\left (2 \, a\right )}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 39, normalized size = 0.83 \[ \frac {1}{4} \, x^{4} + \frac {x^{4}}{x^{4} e^{\left (2 \, a\right )} + 1} - e^{\left (-2 \, a\right )} \log \left (x^{4} e^{\left (2 \, a\right )} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 42, normalized size = 0.89 \[ \frac {x^{4}}{4}-\frac {{\mathrm e}^{-2 a}}{1+{\mathrm e}^{2 a} x^{4}}-{\mathrm e}^{-2 a} \ln \left (1+{\mathrm e}^{2 a} x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 40, normalized size = 0.85 \[ \frac {1}{4} \, x^{4} - e^{\left (-2 \, a\right )} \log \left (x^{4} e^{\left (2 \, a\right )} + 1\right ) - \frac {1}{x^{4} e^{\left (4 \, a\right )} + e^{\left (2 \, a\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 39, normalized size = 0.83 \[ \frac {x^4}{4}-\frac {{\mathrm {e}}^{-2\,a}}{{\mathrm {e}}^{2\,a}\,x^4+1}-{\mathrm {e}}^{-2\,a}\,\ln \left (x^4+{\mathrm {e}}^{-2\,a}\right ) \]
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 \[ \int x^{3} \tanh ^{2}{\left (a + 2 \log {\relax (x )} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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