Optimal. Leaf size=25 \[ \frac{\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \]
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Rubi [A] time = 0.0048654, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {2000} \[ \frac{\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \]
Antiderivative was successfully verified.
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Rule 2000
Rubi steps
\begin{align*} \int \left (a x^3+b x^6\right )^{2/3} \, dx &=\frac{\left (a x^3+b x^6\right )^{5/3}}{5 b x^5}\\ \end{align*}
Mathematica [A] time = 0.0076133, size = 25, normalized size = 1. \[ \frac{\left (x^3 \left (a+b x^3\right )\right )^{5/3}}{5 b x^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 29, normalized size = 1.2 \begin{align*}{\frac{b{x}^{3}+a}{5\,b{x}^{2}} \left ( b{x}^{6}+a{x}^{3} \right ) ^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00102, size = 19, normalized size = 0.76 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.96835, size = 63, normalized size = 2.52 \begin{align*} \frac{{\left (b x^{6} + a x^{3}\right )}^{\frac{2}{3}}{\left (b x^{3} + a\right )}}{5 \, b x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (a x^{3} + b x^{6}\right )^{\frac{2}{3}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11211, size = 19, normalized size = 0.76 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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