Optimal. Leaf size=12 \[ -3 x \left (\frac{b}{x^2}\right )^{2/3} \]
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Rubi [A] time = 0.0014199, 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} \[ -3 x \left (\frac{b}{x^2}\right )^{2/3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (\frac{b}{x^2}\right )^{2/3} \, dx &=\left (\left (\frac{b}{x^2}\right )^{2/3} x^{4/3}\right ) \int \frac{1}{x^{4/3}} \, dx\\ &=-3 \left (\frac{b}{x^2}\right )^{2/3} x\\ \end{align*}
Mathematica [A] time = 0.0013543, size = 12, normalized size = 1. \[ -3 x \left (\frac{b}{x^2}\right )^{2/3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.9 \begin{align*} -3\, \left ({\frac{b}{{x}^{2}}} \right ) ^{2/3}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967578, size = 14, normalized size = 1.17 \begin{align*} -3 \, x \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 = 1.73164, size = 27, normalized size = 2.25 \begin{align*} -3 \, x \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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Sympy [A] time = 0.442713, size = 17, normalized size = 1.42 \begin{align*} - 3 b^{\frac{2}{3}} x \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 \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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