Optimal. Leaf size=29 \[ \frac {x^4}{4}-\frac {1}{2} e^{-2 a} \log \left (e^{2 a} x^4+1\right ) \]
[Out]
________________________________________________________________________________________
Rubi [F] time = 0.03, 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 = {} \[ \int x^3 \tanh (a+2 \log (x)) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int x^3 \tanh (a+2 \log (x)) \, dx &=\int x^3 \tanh (a+2 \log (x)) \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] time = 0.03, size = 64, normalized size = 2.21 \[ -\frac {1}{2} \cosh (2 a) \log \left (x^4 \sinh (a)+x^4 \cosh (a)-\sinh (a)+\cosh (a)\right )+\frac {1}{2} \sinh (2 a) \log \left (x^4 \sinh (a)+x^4 \cosh (a)-\sinh (a)+\cosh (a)\right )+\frac {x^4}{4} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.78, size = 28, normalized size = 0.97 \[ \frac {1}{4} \, {\left (x^{4} e^{\left (2 \, a\right )} - 2 \, \log \left (x^{4} e^{\left (2 \, a\right )} + 1\right )\right )} e^{\left (-2 \, a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.13, size = 23, normalized size = 0.79 \[ \frac {1}{4} \, x^{4} - \frac {1}{2} \, e^{\left (-2 \, a\right )} \log \left (x^{4} e^{\left (2 \, a\right )} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.09, size = 24, normalized size = 0.83 \[ \frac {x^{4}}{4}-\frac {{\mathrm e}^{-2 a} \ln \left (1+{\mathrm e}^{2 a} x^{4}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.32, size = 23, normalized size = 0.79 \[ \frac {1}{4} \, x^{4} - \frac {1}{2} \, e^{\left (-2 \, a\right )} \log \left (x^{4} e^{\left (2 \, a\right )} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.08, size = 21, normalized size = 0.72 \[ \frac {x^4}{4}-\frac {{\mathrm {e}}^{-2\,a}\,\ln \left (x^4+{\mathrm {e}}^{-2\,a}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{3} \tanh {\left (a + 2 \log {\relax (x )} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________