Optimal. Leaf size=43 \[ \frac{1}{5} a^2 b x^{15}+\frac{a^3 x^{12}}{12}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21} \]
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Rubi [A] time = 0.0248982, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{1}{5} a^2 b x^{15}+\frac{a^3 x^{12}}{12}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int x^{11} \left (a+b x^3\right )^3 \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x^3 (a+b x)^3 \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (a^3 x^3+3 a^2 b x^4+3 a b^2 x^5+b^3 x^6\right ) \, dx,x,x^3\right )\\ &=\frac{a^3 x^{12}}{12}+\frac{1}{5} a^2 b x^{15}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21}\\ \end{align*}
Mathematica [A] time = 0.0018367, size = 43, normalized size = 1. \[ \frac{1}{5} a^2 b x^{15}+\frac{a^3 x^{12}}{12}+\frac{1}{6} a b^2 x^{18}+\frac{b^3 x^{21}}{21} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 36, normalized size = 0.8 \begin{align*}{\frac{{a}^{3}{x}^{12}}{12}}+{\frac{{a}^{2}b{x}^{15}}{5}}+{\frac{a{b}^{2}{x}^{18}}{6}}+{\frac{{b}^{3}{x}^{21}}{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.954358, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{21} \, b^{3} x^{21} + \frac{1}{6} \, a b^{2} x^{18} + \frac{1}{5} \, a^{2} b x^{15} + \frac{1}{12} \, a^{3} x^{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54268, size = 88, normalized size = 2.05 \begin{align*} \frac{1}{21} x^{21} b^{3} + \frac{1}{6} x^{18} b^{2} a + \frac{1}{5} x^{15} b a^{2} + \frac{1}{12} x^{12} a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.072994, size = 36, normalized size = 0.84 \begin{align*} \frac{a^{3} x^{12}}{12} + \frac{a^{2} b x^{15}}{5} + \frac{a b^{2} x^{18}}{6} + \frac{b^{3} x^{21}}{21} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13012, size = 47, normalized size = 1.09 \begin{align*} \frac{1}{21} \, b^{3} x^{21} + \frac{1}{6} \, a b^{2} x^{18} + \frac{1}{5} \, a^{2} b x^{15} + \frac{1}{12} \, a^{3} x^{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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