Optimal. Leaf size=14 \[ \frac{3 x}{7 \left (\frac{b}{x^2}\right )^{2/3}} \]
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Rubi [A] time = 0.0013713, 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} \[ \frac{3 x}{7 \left (\frac{b}{x^2}\right )^{2/3}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\left (\frac{b}{x^2}\right )^{2/3}} \, dx &=\frac{\int x^{4/3} \, dx}{\left (\frac{b}{x^2}\right )^{2/3} x^{4/3}}\\ &=\frac{3 x}{7 \left (\frac{b}{x^2}\right )^{2/3}}\\ \end{align*}
Mathematica [A] time = 0.0016934, size = 14, normalized size = 1. \[ \frac{3 x}{7 \left (\frac{b}{x^2}\right )^{2/3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.8 \begin{align*}{\frac{3\,x}{7} \left ({\frac{b}{{x}^{2}}} \right ) ^{-{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.965867, size = 14, normalized size = 1. \begin{align*} \frac{3 \, x}{7 \, \left (\frac{b}{x^{2}}\right )^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.6278, size = 34, normalized size = 2.43 \begin{align*} \frac{3 \, x^{3} \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}}}{7 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.563707, size = 17, normalized size = 1.21 \begin{align*} \frac{3 x}{7 b^{\frac{2}{3}} \left (\frac{1}{x^{2}}\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^{2}}\right )^{\frac{2}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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