Optimal. Leaf size=40 \[ -e^{-a} \tan ^{-1}\left (e^a x^2\right )+\frac {x^2}{e^{2 a} x^4+1}+\frac {x^2}{2} \]
[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 = {} \[ \int x \tanh ^2(a+2 \log (x)) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int x \tanh ^2(a+2 \log (x)) \, dx &=\int x \tanh ^2(a+2 \log (x)) \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.41, size = 41, normalized size = 1.02 \[ \frac {x^2}{e^{2 (a+2 \log (x))}+1}-e^{-a} \tan ^{-1}\left (e^a x^2\right )+\frac {x^2}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 50, normalized size = 1.25 \[ \frac {x^{6} e^{\left (3 \, a\right )} + 3 \, x^{2} e^{a} - 2 \, {\left (x^{4} e^{\left (2 \, a\right )} + 1\right )} \arctan \left (x^{2} e^{a}\right )}{2 \, {\left (x^{4} e^{\left (3 \, a\right )} + e^{a}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.12, size = 35, normalized size = 0.88 \[ \frac {1}{2} \, x^{2} - \arctan \left (x^{2} e^{a}\right ) e^{\left (-a\right )} + \frac {x^{2}}{x^{4} e^{\left (2 \, a\right )} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.09, size = 57, normalized size = 1.42 \[ \frac {x^{2}}{2}+\frac {x^{2}}{1+{\mathrm e}^{2 a} x^{4}}+\frac {i {\mathrm e}^{-a} \ln \left ({\mathrm e}^{a} x^{2}-i\right )}{2}-\frac {i {\mathrm e}^{-a} \ln \left ({\mathrm e}^{a} x^{2}+i\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 35, normalized size = 0.88 \[ \frac {1}{2} \, x^{2} - \arctan \left (x^{2} e^{a}\right ) e^{\left (-a\right )} + \frac {x^{2}}{x^{4} e^{\left (2 \, a\right )} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.05, size = 41, normalized size = 1.02 \[ \frac {x^2}{{\mathrm {e}}^{2\,a}\,x^4+1}-\frac {\mathrm {atan}\left (x^2\,\sqrt {{\mathrm {e}}^{2\,a}}\right )}{\sqrt {{\mathrm {e}}^{2\,a}}}+\frac {x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x \tanh ^{2}{\left (a + 2 \log {\relax (x )} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________