Optimal. Leaf size=17 \[ \frac{2}{11} b x^4 \sqrt{b x^3} \]
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Rubi [A] time = 0.0016906, antiderivative size = 17, 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} \[ \frac{2}{11} b x^4 \sqrt{b x^3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (b x^3\right )^{3/2} \, dx &=\frac{\left (b \sqrt{b x^3}\right ) \int x^{9/2} \, dx}{x^{3/2}}\\ &=\frac{2}{11} b x^4 \sqrt{b x^3}\\ \end{align*}
Mathematica [A] time = 0.0012278, size = 14, normalized size = 0.82 \[ \frac{2}{11} x \left (b x^3\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.7 \begin{align*}{\frac{2\,x}{11} \left ( b{x}^{3} \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96569, size = 14, normalized size = 0.82 \begin{align*} \frac{2}{11} \, \left (b x^{3}\right )^{\frac{3}{2}} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67623, size = 32, normalized size = 1.88 \begin{align*} \frac{2}{11} \, \sqrt{b x^{3}} b x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.493833, size = 15, normalized size = 0.88 \begin{align*} \frac{2 b^{\frac{3}{2}} x \left (x^{3}\right )^{\frac{3}{2}}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14539, size = 18, normalized size = 1.06 \begin{align*} \frac{2}{11} \, \sqrt{b x} b x^{5} \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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