Optimal. Leaf size=12 \[ 3 x \sqrt [3]{\frac{b}{x^2}} \]
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Rubi [A] time = 0.0015893, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 30} \[ 3 x \sqrt [3]{\frac{b}{x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \sqrt [3]{\frac{b}{x^2}} \, dx &=\left (\sqrt [3]{\frac{b}{x^2}} x^{2/3}\right ) \int \frac{1}{x^{2/3}} \, dx\\ &=3 \sqrt [3]{\frac{b}{x^2}} x\\ \end{align*}
Mathematica [A] time = 0.0009864, size = 12, normalized size = 1. \[ 3 x \sqrt [3]{\frac{b}{x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 0.9 \begin{align*} 3\,\sqrt [3]{{\frac{b}{{x}^{2}}}}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.973353, size = 14, normalized size = 1.17 \begin{align*} 3 \, x \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.63219, size = 26, normalized size = 2.17 \begin{align*} 3 \, x \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.45948, size = 15, normalized size = 1.25 \begin{align*} 3 \sqrt [3]{b} x \sqrt [3]{\frac{1}{x^{2}}} \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 \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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