Optimal. Leaf size=14 \[ \frac{1}{2} x \sqrt [3]{b x^3} \]
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Rubi [A] time = 0.0013163, 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} \[ \frac{1}{2} x \sqrt [3]{b x^3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \sqrt [3]{b x^3} \, dx &=\frac{\sqrt [3]{b x^3} \int x \, dx}{x}\\ &=\frac{1}{2} x \sqrt [3]{b x^3}\\ \end{align*}
Mathematica [A] time = 0.0010876, size = 14, normalized size = 1. \[ \frac{1}{2} x \sqrt [3]{b x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 0.8 \begin{align*}{\frac{x}{2}\sqrt [3]{b{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.965428, size = 14, normalized size = 1. \begin{align*} \frac{1}{2} \, \left (b x^{3}\right )^{\frac{1}{3}} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.65456, size = 28, normalized size = 2. \begin{align*} \frac{1}{2} \, \left (b x^{3}\right )^{\frac{1}{3}} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.217048, size = 14, normalized size = 1. \begin{align*} \frac{\sqrt [3]{b} x \sqrt [3]{x^{3}}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14929, size = 11, normalized size = 0.79 \begin{align*} \frac{1}{2} \, b^{\frac{1}{3}} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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