Optimal. Leaf size=51 \[ \frac{9}{11} a^2 b x^{11/3}+\frac{3}{8} a^3 x^{8/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{3}{17} b^3 x^{17/3} \]
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Rubi [A] time = 0.0104423, antiderivative size = 51, 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} \[ \frac{9}{11} a^2 b x^{11/3}+\frac{3}{8} a^3 x^{8/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{3}{17} b^3 x^{17/3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int x^{5/3} (a+b x)^3 \, dx &=\int \left (a^3 x^{5/3}+3 a^2 b x^{8/3}+3 a b^2 x^{11/3}+b^3 x^{14/3}\right ) \, dx\\ &=\frac{3}{8} a^3 x^{8/3}+\frac{9}{11} a^2 b x^{11/3}+\frac{9}{14} a b^2 x^{14/3}+\frac{3}{17} b^3 x^{17/3}\\ \end{align*}
Mathematica [A] time = 0.0117228, size = 39, normalized size = 0.76 \[ \frac{3 x^{8/3} \left (2856 a^2 b x+1309 a^3+2244 a b^2 x^2+616 b^3 x^3\right )}{10472} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 36, normalized size = 0.7 \begin{align*}{\frac{1848\,{b}^{3}{x}^{3}+6732\,a{b}^{2}{x}^{2}+8568\,{a}^{2}bx+3927\,{a}^{3}}{10472}{x}^{{\frac{8}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.42024, size = 47, normalized size = 0.92 \begin{align*} \frac{3}{17} \, b^{3} x^{\frac{17}{3}} + \frac{9}{14} \, a b^{2} x^{\frac{14}{3}} + \frac{9}{11} \, a^{2} b x^{\frac{11}{3}} + \frac{3}{8} \, a^{3} x^{\frac{8}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54968, size = 108, normalized size = 2.12 \begin{align*} \frac{3}{10472} \,{\left (616 \, b^{3} x^{5} + 2244 \, a b^{2} x^{4} + 2856 \, a^{2} b x^{3} + 1309 \, a^{3} 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 = 7.31497, size = 49, normalized size = 0.96 \begin{align*} \frac{3 a^{3} x^{\frac{8}{3}}}{8} + \frac{9 a^{2} b x^{\frac{11}{3}}}{11} + \frac{9 a b^{2} x^{\frac{14}{3}}}{14} + \frac{3 b^{3} x^{\frac{17}{3}}}{17} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07897, size = 47, normalized size = 0.92 \begin{align*} \frac{3}{17} \, b^{3} x^{\frac{17}{3}} + \frac{9}{14} \, a b^{2} x^{\frac{14}{3}} + \frac{9}{11} \, a^{2} b x^{\frac{11}{3}} + \frac{3}{8} \, a^{3} x^{\frac{8}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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