Optimal. Leaf size=21 \[ -\frac{\left (a+b x^3\right )^{2/3}}{2 a x^2} \]
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Rubi [A] time = 0.0048383, antiderivative size = 21, 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} \[ -\frac{\left (a+b x^3\right )^{2/3}}{2 a x^2} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{x^3 \sqrt [3]{a+b x^3}} \, dx &=-\frac{\left (a+b x^3\right )^{2/3}}{2 a x^2}\\ \end{align*}
Mathematica [A] time = 0.0036308, size = 21, normalized size = 1. \[ -\frac{\left (a+b x^3\right )^{2/3}}{2 a x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 18, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,a{x}^{2}} \left ( b{x}^{3}+a \right ) ^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.97992, size = 23, normalized size = 1.1 \begin{align*} -\frac{{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{2 \, a x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51147, size = 43, normalized size = 2.05 \begin{align*} -\frac{{\left (b x^{3} + a\right )}^{\frac{2}{3}}}{2 \, a x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.653812, size = 31, normalized size = 1.48 \begin{align*} \frac{b^{\frac{2}{3}} \left (\frac{a}{b x^{3}} + 1\right )^{\frac{2}{3}} \Gamma \left (- \frac{2}{3}\right )}{3 a \Gamma \left (\frac{1}{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{1}{3}} x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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