Optimal. Leaf size=35 \[ \frac{x^6}{6}-\frac{4 x^3}{3}-\frac{1}{6} \log \left (x^3+1\right )+\frac{9}{2} \log \left (x^3+3\right ) \]
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Rubi [A] time = 0.024081, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {1357, 701, 632, 31} \[ \frac{x^6}{6}-\frac{4 x^3}{3}-\frac{1}{6} \log \left (x^3+1\right )+\frac{9}{2} \log \left (x^3+3\right ) \]
Antiderivative was successfully verified.
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Rule 1357
Rule 701
Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{x^{11}}{3+4 x^3+x^6} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{x^3}{3+4 x+x^2} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (-4+x+\frac{12+13 x}{3+4 x+x^2}\right ) \, dx,x,x^3\right )\\ &=-\frac{4 x^3}{3}+\frac{x^6}{6}+\frac{1}{3} \operatorname{Subst}\left (\int \frac{12+13 x}{3+4 x+x^2} \, dx,x,x^3\right )\\ &=-\frac{4 x^3}{3}+\frac{x^6}{6}-\frac{1}{6} \operatorname{Subst}\left (\int \frac{1}{1+x} \, dx,x,x^3\right )+\frac{9}{2} \operatorname{Subst}\left (\int \frac{1}{3+x} \, dx,x,x^3\right )\\ &=-\frac{4 x^3}{3}+\frac{x^6}{6}-\frac{1}{6} \log \left (1+x^3\right )+\frac{9}{2} \log \left (3+x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0061133, size = 35, normalized size = 1. \[ \frac{x^6}{6}-\frac{4 x^3}{3}-\frac{1}{6} \log \left (x^3+1\right )+\frac{9}{2} \log \left (x^3+3\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 28, normalized size = 0.8 \begin{align*} -{\frac{4\,{x}^{3}}{3}}+{\frac{{x}^{6}}{6}}-{\frac{\ln \left ({x}^{3}+1 \right ) }{6}}+{\frac{9\,\ln \left ({x}^{3}+3 \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.2259, size = 36, normalized size = 1.03 \begin{align*} \frac{1}{6} \, x^{6} - \frac{4}{3} \, x^{3} + \frac{9}{2} \, \log \left (x^{3} + 3\right ) - \frac{1}{6} \, \log \left (x^{3} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41851, size = 77, normalized size = 2.2 \begin{align*} \frac{1}{6} \, x^{6} - \frac{4}{3} \, x^{3} + \frac{9}{2} \, \log \left (x^{3} + 3\right ) - \frac{1}{6} \, \log \left (x^{3} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.120889, size = 29, normalized size = 0.83 \begin{align*} \frac{x^{6}}{6} - \frac{4 x^{3}}{3} - \frac{\log{\left (x^{3} + 1 \right )}}{6} + \frac{9 \log{\left (x^{3} + 3 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09476, size = 39, normalized size = 1.11 \begin{align*} \frac{1}{6} \, x^{6} - \frac{4}{3} \, x^{3} + \frac{9}{2} \, \log \left ({\left | x^{3} + 3 \right |}\right ) - \frac{1}{6} \, \log \left ({\left | x^{3} + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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