Optimal. Leaf size=15 \[ \frac{\sqrt [3]{a+b x^3}}{b} \]
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Rubi [A] time = 0.004248, antiderivative size = 15, 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 = {261} \[ \frac{\sqrt [3]{a+b x^3}}{b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^2}{\left (a+b x^3\right )^{2/3}} \, dx &=\frac{\sqrt [3]{a+b x^3}}{b}\\ \end{align*}
Mathematica [A] time = 0.0030014, size = 15, normalized size = 1. \[ \frac{\sqrt [3]{a+b x^3}}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.9 \begin{align*}{\frac{1}{b}\sqrt [3]{b{x}^{3}+a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05325, size = 18, normalized size = 1.2 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.43783, size = 28, normalized size = 1.87 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.538253, size = 20, normalized size = 1.33 \begin{align*} \begin{cases} \frac{\sqrt [3]{a + b x^{3}}}{b} & \text{for}\: b \neq 0 \\\frac{x^{3}}{3 a^{\frac{2}{3}}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10198, size = 18, normalized size = 1.2 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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