Optimal. Leaf size=36 \[ \frac{3}{7} a^2 x^{7/3}+\frac{3}{5} a b x^{10/3}+\frac{3}{13} b^2 x^{13/3} \]
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Rubi [A] time = 0.0070806, 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} \[ \frac{3}{7} a^2 x^{7/3}+\frac{3}{5} a b x^{10/3}+\frac{3}{13} b^2 x^{13/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{4/3} (a+b x)^2 \, dx &=\int \left (a^2 x^{4/3}+2 a b x^{7/3}+b^2 x^{10/3}\right ) \, dx\\ &=\frac{3}{7} a^2 x^{7/3}+\frac{3}{5} a b x^{10/3}+\frac{3}{13} b^2 x^{13/3}\\ \end{align*}
Mathematica [A] time = 0.0076244, size = 28, normalized size = 0.78 \[ \frac{3}{455} x^{7/3} \left (65 a^2+91 a b x+35 b^2 x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 25, normalized size = 0.7 \begin{align*}{\frac{105\,{b}^{2}{x}^{2}+273\,abx+195\,{a}^{2}}{455}{x}^{{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03683, size = 32, normalized size = 0.89 \begin{align*} \frac{3}{13} \, b^{2} x^{\frac{13}{3}} + \frac{3}{5} \, a b x^{\frac{10}{3}} + \frac{3}{7} \, a^{2} x^{\frac{7}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46162, size = 73, normalized size = 2.03 \begin{align*} \frac{3}{455} \,{\left (35 \, b^{2} x^{4} + 91 \, a b x^{3} + 65 \, a^{2} x^{2}\right )} x^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 3.16779, size = 34, normalized size = 0.94 \begin{align*} \frac{3 a^{2} x^{\frac{7}{3}}}{7} + \frac{3 a b x^{\frac{10}{3}}}{5} + \frac{3 b^{2} x^{\frac{13}{3}}}{13} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05798, size = 32, normalized size = 0.89 \begin{align*} \frac{3}{13} \, b^{2} x^{\frac{13}{3}} + \frac{3}{5} \, a b x^{\frac{10}{3}} + \frac{3}{7} \, a^{2} x^{\frac{7}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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