Optimal. Leaf size=14 \[ \frac{2 (b x)^{5/2}}{5 b} \]
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Rubi [A] time = 0.0013268, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {32} \[ \frac{2 (b x)^{5/2}}{5 b} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int (b x)^{3/2} \, dx &=\frac{2 (b x)^{5/2}}{5 b}\\ \end{align*}
Mathematica [A] time = 0.0010862, size = 12, normalized size = 0.86 \[ \frac{2}{5} x (b x)^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 9, normalized size = 0.6 \begin{align*}{\frac{2\,x}{5} \left ( bx \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.999249, size = 14, normalized size = 1. \begin{align*} \frac{2 \, \left (b x\right )^{\frac{5}{2}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72605, size = 28, normalized size = 2. \begin{align*} \frac{2}{5} \, \sqrt{b x} b x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.068235, size = 10, normalized size = 0.71 \begin{align*} \frac{2 \left (b x\right )^{\frac{5}{2}}}{5 b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17478, size = 15, normalized size = 1.07 \begin{align*} \frac{2}{5} \, \sqrt{b x} b x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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