Optimal. Leaf size=21 \[ \frac{3}{5} a x^{5/3}+\frac{3}{8} b x^{8/3} \]
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Rubi [A] time = 0.003643, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{3}{5} a x^{5/3}+\frac{3}{8} b x^{8/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{2/3} (a+b x) \, dx &=\int \left (a x^{2/3}+b x^{5/3}\right ) \, dx\\ &=\frac{3}{5} a x^{5/3}+\frac{3}{8} b x^{8/3}\\ \end{align*}
Mathematica [A] time = 0.0046576, size = 17, normalized size = 0.81 \[ \frac{3}{40} x^{5/3} (8 a+5 b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.7 \begin{align*}{\frac{15\,bx+24\,a}{40}{x}^{{\frac{5}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0489, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{8} \, b x^{\frac{8}{3}} + \frac{3}{5} \, a x^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54449, size = 43, normalized size = 2.05 \begin{align*} \frac{3}{40} \,{\left (5 \, b x^{2} + 8 \, a 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 = 0.485269, size = 19, normalized size = 0.9 \begin{align*} \frac{3 a x^{\frac{5}{3}}}{5} + \frac{3 b x^{\frac{8}{3}}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05589, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{8} \, b x^{\frac{8}{3}} + \frac{3}{5} \, a x^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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