Optimal. Leaf size=21 \[ \frac{3}{8} a x^{8/3}+\frac{3}{11} b x^{11/3} \]
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Rubi [A] time = 0.0035423, 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} \[ \frac{3}{8} a x^{8/3}+\frac{3}{11} b x^{11/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{5/3} (a+b x) \, dx &=\int \left (a x^{5/3}+b x^{8/3}\right ) \, dx\\ &=\frac{3}{8} a x^{8/3}+\frac{3}{11} b x^{11/3}\\ \end{align*}
Mathematica [A] time = 0.00556, size = 17, normalized size = 0.81 \[ \frac{3}{88} x^{8/3} (11 a+8 b x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 14, normalized size = 0.7 \begin{align*}{\frac{24\,bx+33\,a}{88}{x}^{{\frac{8}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07222, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{11} \, b x^{\frac{11}{3}} + \frac{3}{8} \, a x^{\frac{8}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38988, size = 47, normalized size = 2.24 \begin{align*} \frac{3}{88} \,{\left (8 \, b x^{3} + 11 \, a 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 = 2.21241, size = 19, normalized size = 0.9 \begin{align*} \frac{3 a x^{\frac{8}{3}}}{8} + \frac{3 b x^{\frac{11}{3}}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04928, size = 18, normalized size = 0.86 \begin{align*} \frac{3}{11} \, b x^{\frac{11}{3}} + \frac{3}{8} \, a x^{\frac{8}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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