Optimal. Leaf size=17 \[ \frac{1}{3} b x^2 \sqrt{b x^2} \]
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Rubi [A] time = 0.0016634, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {15, 30} \[ \frac{1}{3} b x^2 \sqrt{b x^2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{\left (b x^2\right )^{3/2}}{x} \, dx &=\frac{\left (b \sqrt{b x^2}\right ) \int x^2 \, dx}{x}\\ &=\frac{1}{3} b x^2 \sqrt{b x^2}\\ \end{align*}
Mathematica [A] time = 0.0009414, size = 17, normalized size = 1. \[ \frac{1}{3} b x^2 \sqrt{b x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 10, normalized size = 0.6 \begin{align*}{\frac{1}{3} \left ( b{x}^{2} \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.2212, size = 31, normalized size = 1.82 \begin{align*} \frac{1}{3} \, \sqrt{b x^{2}} b x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.491118, size = 12, normalized size = 0.71 \begin{align*} \frac{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22163, size = 14, normalized size = 0.82 \begin{align*} \frac{1}{3} \, b^{\frac{3}{2}} x^{3} \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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