Optimal. Leaf size=12 \[ x \left (-\left (\frac{b}{x^3}\right )^{2/3}\right ) \]
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Rubi [A] time = 0.0014428, 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} \[ x \left (-\left (\frac{b}{x^3}\right )^{2/3}\right ) \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (\frac{b}{x^3}\right )^{2/3} \, dx &=\left (\left (\frac{b}{x^3}\right )^{2/3} x^2\right ) \int \frac{1}{x^2} \, dx\\ &=-\left (\frac{b}{x^3}\right )^{2/3} x\\ \end{align*}
Mathematica [A] time = 0.0011566, size = 12, normalized size = 1. \[ x \left (-\left (\frac{b}{x^3}\right )^{2/3}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 0.9 \begin{align*} - \left ({\frac{b}{{x}^{3}}} \right ) ^{{\frac{2}{3}}}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.992274, size = 14, normalized size = 1.17 \begin{align*} -x \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 = 1.67286, size = 24, normalized size = 2. \begin{align*} -x \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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Sympy [A] time = 0.424078, size = 15, normalized size = 1.25 \begin{align*} - b^{\frac{2}{3}} x \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 \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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