Optimal. Leaf size=36 \[ \frac{3}{8} a^2 x^{8/3}+\frac{6}{11} a b x^{11/3}+\frac{3}{14} b^2 x^{14/3} \]
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Rubi [A] time = 0.0067997, antiderivative size = 36, 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} \[ \frac{3}{8} a^2 x^{8/3}+\frac{6}{11} a b x^{11/3}+\frac{3}{14} b^2 x^{14/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{5/3} (a+b x)^2 \, dx &=\int \left (a^2 x^{5/3}+2 a b x^{8/3}+b^2 x^{11/3}\right ) \, dx\\ &=\frac{3}{8} a^2 x^{8/3}+\frac{6}{11} a b x^{11/3}+\frac{3}{14} b^2 x^{14/3}\\ \end{align*}
Mathematica [A] time = 0.0083215, size = 28, normalized size = 0.78 \[ \frac{3}{616} x^{8/3} \left (77 a^2+112 a b x+44 b^2 x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 25, normalized size = 0.7 \begin{align*}{\frac{132\,{b}^{2}{x}^{2}+336\,abx+231\,{a}^{2}}{616}{x}^{{\frac{8}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00203, size = 32, normalized size = 0.89 \begin{align*} \frac{3}{14} \, b^{2} x^{\frac{14}{3}} + \frac{6}{11} \, a b x^{\frac{11}{3}} + \frac{3}{8} \, a^{2} x^{\frac{8}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46021, size = 74, normalized size = 2.06 \begin{align*} \frac{3}{616} \,{\left (44 \, b^{2} x^{4} + 112 \, a b x^{3} + 77 \, a^{2} x^{2}\right )} x^{\frac{2}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 4.0259, size = 34, normalized size = 0.94 \begin{align*} \frac{3 a^{2} x^{\frac{8}{3}}}{8} + \frac{6 a b x^{\frac{11}{3}}}{11} + \frac{3 b^{2} x^{\frac{14}{3}}}{14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07298, size = 32, normalized size = 0.89 \begin{align*} \frac{3}{14} \, b^{2} x^{\frac{14}{3}} + \frac{6}{11} \, a b x^{\frac{11}{3}} + \frac{3}{8} \, a^{2} x^{\frac{8}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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