Optimal. Leaf size=12 \[ \frac{3 x}{\sqrt [3]{b x^2}} \]
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Rubi [A] time = 0.0013559, 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} \[ \frac{3 x}{\sqrt [3]{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt [3]{b x^2}} \, dx &=\frac{x^{2/3} \int \frac{1}{x^{2/3}} \, dx}{\sqrt [3]{b x^2}}\\ &=\frac{3 x}{\sqrt [3]{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0013431, size = 12, normalized size = 1. \[ \frac{3 x}{\sqrt [3]{b x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 0.9 \begin{align*} 3\,{\frac{x}{\sqrt [3]{b{x}^{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.975631, size = 14, normalized size = 1.17 \begin{align*} \frac{3 \, x}{\left (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 = 1.66034, size = 31, normalized size = 2.58 \begin{align*} \frac{3 \, \left (b x^{2}\right )^{\frac{2}{3}}}{b x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.369437, size = 14, normalized size = 1.17 \begin{align*} \frac{3 x}{\sqrt [3]{b} \sqrt [3]{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 \frac{1}{\left (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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