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 = 0.02, antiderivative size = 35, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, 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 31
Rule 632
Rule 701
Rule 1357
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*}
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Mathematica [A] time = 0.01, size = 35, normalized size = 1.00 \[ \frac {x^6}{6}-\frac {4 x^3}{3}-\frac {1}{6} \log \left (x^3+1\right )+\frac {9}{2} \log \left (x^3+3\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.09, size = 27, normalized size = 0.77 \[ \frac {1}{6} \, x^{6} - \frac {4}{3} \, x^{3} + \frac {9}{2} \, \log \left (x^{3} + 3\right ) - \frac {1}{6} \, \log \left (x^{3} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 29, normalized size = 0.83 \[ \frac {1}{6} \, x^{6} - \frac {4}{3} \, x^{3} + \frac {9}{2} \, \log \left ({\left | x^{3} + 3 \right |}\right ) - \frac {1}{6} \, \log \left ({\left | x^{3} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 28, normalized size = 0.80 \[ \frac {x^{6}}{6}-\frac {4 x^{3}}{3}-\frac {\ln \left (x^{3}+1\right )}{6}+\frac {9 \ln \left (x^{3}+3\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 27, normalized size = 0.77 \[ \frac {1}{6} \, x^{6} - \frac {4}{3} \, x^{3} + \frac {9}{2} \, \log \left (x^{3} + 3\right ) - \frac {1}{6} \, \log \left (x^{3} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.25, size = 27, normalized size = 0.77 \[ \frac {9\,\ln \left (x^3+3\right )}{2}-\frac {\ln \left (x^3+1\right )}{6}-\frac {4\,x^3}{3}+\frac {x^6}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 29, normalized size = 0.83 \[ \frac {x^{6}}{6} - \frac {4 x^{3}}{3} - \frac {\log {\left (x^{3} + 1 \right )}}{6} + \frac {9 \log {\left (x^{3} + 3 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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