Optimal. Leaf size=36 \[ \frac{3}{5} a^2 x^{5/3}+\frac{3}{4} a b x^{8/3}+\frac{3}{11} b^2 x^{11/3} \]
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Rubi [A] time = 0.0068258, 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} \[ \frac{3}{5} a^2 x^{5/3}+\frac{3}{4} a b x^{8/3}+\frac{3}{11} b^2 x^{11/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{2/3} (a+b x)^2 \, dx &=\int \left (a^2 x^{2/3}+2 a b x^{5/3}+b^2 x^{8/3}\right ) \, dx\\ &=\frac{3}{5} a^2 x^{5/3}+\frac{3}{4} a b x^{8/3}+\frac{3}{11} b^2 x^{11/3}\\ \end{align*}
Mathematica [A] time = 0.0074095, size = 28, normalized size = 0.78 \[ \frac{3}{220} x^{5/3} \left (44 a^2+55 a b x+20 b^2 x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 0.7 \begin{align*}{\frac{60\,{b}^{2}{x}^{2}+165\,abx+132\,{a}^{2}}{220}{x}^{{\frac{5}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04631, size = 32, normalized size = 0.89 \begin{align*} \frac{3}{11} \, b^{2} x^{\frac{11}{3}} + \frac{3}{4} \, a b x^{\frac{8}{3}} + \frac{3}{5} \, a^{2} x^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51761, size = 70, normalized size = 1.94 \begin{align*} \frac{3}{220} \,{\left (20 \, b^{2} x^{3} + 55 \, a b x^{2} + 44 \, a^{2} 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 = 1.29595, size = 34, normalized size = 0.94 \begin{align*} \frac{3 a^{2} x^{\frac{5}{3}}}{5} + \frac{3 a b x^{\frac{8}{3}}}{4} + \frac{3 b^{2} x^{\frac{11}{3}}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06283, size = 32, normalized size = 0.89 \begin{align*} \frac{3}{11} \, b^{2} x^{\frac{11}{3}} + \frac{3}{4} \, a b x^{\frac{8}{3}} + \frac{3}{5} \, a^{2} x^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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