Optimal. Leaf size=19 \[ -\frac{\sqrt [3]{a+b x^3}}{a x} \]
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Rubi [A] time = 0.0048431, antiderivative size = 19, 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 = {264} \[ -\frac{\sqrt [3]{a+b x^3}}{a x} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^2 \left (a+b x^3\right )^{2/3}} \, dx &=-\frac{\sqrt [3]{a+b x^3}}{a x}\\ \end{align*}
Mathematica [A] time = 0.003754, size = 19, normalized size = 1. \[ -\frac{\sqrt [3]{a+b x^3}}{a x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 18, normalized size = 1. \begin{align*} -{\frac{1}{ax}\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 = 1.01348, size = 23, normalized size = 1.21 \begin{align*} -\frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{a x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.50717, size = 35, normalized size = 1.84 \begin{align*} -\frac{{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{a x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.612493, size = 31, normalized size = 1.63 \begin{align*} \frac{\sqrt [3]{b} \sqrt [3]{\frac{a}{b x^{3}} + 1} \Gamma \left (- \frac{1}{3}\right )}{3 a \Gamma \left (\frac{2}{3}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b x^{3} + a\right )}^{\frac{2}{3}} x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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