Optimal. Leaf size=51 \[ \frac{9}{8} a^2 b x^{8/3}+\frac{3}{5} a^3 x^{5/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{3}{14} b^3 x^{14/3} \]
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Rubi [A] time = 0.010782, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ \frac{9}{8} a^2 b x^{8/3}+\frac{3}{5} a^3 x^{5/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{3}{14} b^3 x^{14/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{2/3} (a+b x)^3 \, dx &=\int \left (a^3 x^{2/3}+3 a^2 b x^{5/3}+3 a b^2 x^{8/3}+b^3 x^{11/3}\right ) \, dx\\ &=\frac{3}{5} a^3 x^{5/3}+\frac{9}{8} a^2 b x^{8/3}+\frac{9}{11} a b^2 x^{11/3}+\frac{3}{14} b^3 x^{14/3}\\ \end{align*}
Mathematica [A] time = 0.0103705, size = 39, normalized size = 0.76 \[ \frac{3 x^{5/3} \left (1155 a^2 b x+616 a^3+840 a b^2 x^2+220 b^3 x^3\right )}{3080} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 36, normalized size = 0.7 \begin{align*}{\frac{660\,{b}^{3}{x}^{3}+2520\,a{b}^{2}{x}^{2}+3465\,{a}^{2}bx+1848\,{a}^{3}}{3080}{x}^{{\frac{5}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.18694, size = 47, normalized size = 0.92 \begin{align*} \frac{3}{14} \, b^{3} x^{\frac{14}{3}} + \frac{9}{11} \, a b^{2} x^{\frac{11}{3}} + \frac{9}{8} \, a^{2} b x^{\frac{8}{3}} + \frac{3}{5} \, a^{3} x^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45842, size = 101, normalized size = 1.98 \begin{align*} \frac{3}{3080} \,{\left (220 \, b^{3} x^{4} + 840 \, a b^{2} x^{3} + 1155 \, a^{2} b x^{2} + 616 \, a^{3} x\right )} x^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.50533, size = 49, normalized size = 0.96 \begin{align*} \frac{3 a^{3} x^{\frac{5}{3}}}{5} + \frac{9 a^{2} b x^{\frac{8}{3}}}{8} + \frac{9 a b^{2} x^{\frac{11}{3}}}{11} + \frac{3 b^{3} x^{\frac{14}{3}}}{14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05635, size = 47, normalized size = 0.92 \begin{align*} \frac{3}{14} \, b^{3} x^{\frac{14}{3}} + \frac{9}{11} \, a b^{2} x^{\frac{11}{3}} + \frac{9}{8} \, a^{2} b x^{\frac{8}{3}} + \frac{3}{5} \, a^{3} x^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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