Optimal. Leaf size=14 \[ \frac{2}{5} x \sqrt{b x^3} \]
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Rubi [A] time = 0.0015145, 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} \[ \frac{2}{5} x \sqrt{b x^3} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \sqrt{b x^3} \, dx &=\frac{\sqrt{b x^3} \int x^{3/2} \, dx}{x^{3/2}}\\ &=\frac{2}{5} x \sqrt{b x^3}\\ \end{align*}
Mathematica [A] time = 0.0011297, size = 14, normalized size = 1. \[ \frac{2}{5} x \sqrt{b x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 11, normalized size = 0.8 \begin{align*}{\frac{2\,x}{5}\sqrt{b{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963388, size = 14, normalized size = 1. \begin{align*} \frac{2}{5} \, \sqrt{b x^{3}} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67164, size = 26, normalized size = 1.86 \begin{align*} \frac{2}{5} \, \sqrt{b x^{3}} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.198555, size = 15, normalized size = 1.07 \begin{align*} \frac{2 \sqrt{b} x \sqrt{x^{3}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19425, size = 16, normalized size = 1.14 \begin{align*} \frac{2}{5} \, \sqrt{b x} x^{2} \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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