Optimal. Leaf size=14 \[ \frac{x}{3 \left (\frac{b}{x^3}\right )^{2/3}} \]
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Rubi [A] time = 0.001497, antiderivative size = 14, 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} \[ \frac{x}{3 \left (\frac{b}{x^3}\right )^{2/3}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\left (\frac{b}{x^3}\right )^{2/3}} \, dx &=\frac{\int x^2 \, dx}{\left (\frac{b}{x^3}\right )^{2/3} x^2}\\ &=\frac{x}{3 \left (\frac{b}{x^3}\right )^{2/3}}\\ \end{align*}
Mathematica [A] time = 0.0016679, size = 14, normalized size = 1. \[ \frac{x}{3 \left (\frac{b}{x^3}\right )^{2/3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 11, normalized size = 0.8 \begin{align*}{\frac{x}{3} \left ({\frac{b}{{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 = 0.954741, size = 14, normalized size = 1. \begin{align*} \frac{x}{3 \, \left (\frac{b}{x^{3}}\right )^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.75821, size = 34, normalized size = 2.43 \begin{align*} \frac{x^{4} \left (\frac{b}{x^{3}}\right )^{\frac{1}{3}}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.551072, size = 15, normalized size = 1.07 \begin{align*} \frac{x}{3 b^{\frac{2}{3}} \left (\frac{1}{x^{3}}\right )^{\frac{2}{3}}} \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 (\frac{b}{x^{3}}\right )^{\frac{2}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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