Optimal. Leaf size=14 \[ \frac {3 x}{4 \sqrt [3]{\frac {b}{x}}} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {3 x}{4 \sqrt [3]{\frac {b}{x}}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 15, normalized size = 1.07 \[ \frac {3 \, x^{2} \left (\frac {b}{x}\right )^{\frac {2}{3}}}{4 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 10, normalized size = 0.71 \[ \frac {3 \, x}{4 \, \left (\frac {b}{x}\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.79 \[ \frac {3 x}{4 \left (\frac {b}{x}\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 10, normalized size = 0.71 \[ \frac {3 \, x}{4 \, \left (\frac {b}{x}\right )^{\frac {1}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.92, size = 15, normalized size = 1.07 \[ \frac {3\,x^2\,{\left (\frac {b}{x}\right )}^{2/3}}{4\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.43, size = 15, normalized size = 1.07 \[ \frac {3 x}{4 \sqrt [3]{b} \sqrt [3]{\frac {1}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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