Optimal. Leaf size=14 \[ \frac{3 x}{4 \sqrt [3]{\frac{b}{x}}} \]
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Rubi [A] time = 0.0015995, 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} \[ \frac{3 x}{4 \sqrt [3]{\frac{b}{x}}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt [3]{\frac{b}{x}}} \, dx &=\frac{\int \sqrt [3]{x} \, dx}{\sqrt [3]{\frac{b}{x}} \sqrt [3]{x}}\\ &=\frac{3 x}{4 \sqrt [3]{\frac{b}{x}}}\\ \end{align*}
Mathematica [A] time = 0.002079, size = 14, normalized size = 1. \[ \frac{3 x}{4 \sqrt [3]{\frac{b}{x}}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.8 \begin{align*}{\frac{3\,x}{4}{\frac{1}{\sqrt [3]{{\frac{b}{x}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.997423, size = 14, normalized size = 1. \begin{align*} \frac{3 \, x}{4 \, \left (\frac{b}{x}\right )^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66937, size = 31, normalized size = 2.21 \begin{align*} \frac{3 \, x^{2} \left (\frac{b}{x}\right )^{\frac{2}{3}}}{4 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.371547, size = 15, normalized size = 1.07 \begin{align*} \frac{3 x}{4 \sqrt [3]{b} \sqrt [3]{\frac{1}{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16362, size = 14, normalized size = 1. \begin{align*} \frac{3 \, x}{4 \, \left (\frac{b}{x}\right )^{\frac{1}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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