Optimal. Leaf size=12 \[ -2 b \sqrt{\frac{b}{x}} \]
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Rubi [A] time = 0.0016709, antiderivative size = 12, 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} \[ -2 b \sqrt{\frac{b}{x}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (\frac{b}{x}\right )^{3/2} \, dx &=\left (b \sqrt{\frac{b}{x}} \sqrt{x}\right ) \int \frac{1}{x^{3/2}} \, dx\\ &=-2 b \sqrt{\frac{b}{x}}\\ \end{align*}
Mathematica [A] time = 0.0011895, size = 12, normalized size = 1. \[ -2 x \left (\frac{b}{x}\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.9 \begin{align*} -2\,x \left ({\frac{b}{x}} \right ) ^{3/2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.958135, size = 14, normalized size = 1.17 \begin{align*} -2 \, x \left (\frac{b}{x}\right )^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72821, size = 22, normalized size = 1.83 \begin{align*} -2 \, b \sqrt{\frac{b}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.504955, size = 15, normalized size = 1.25 \begin{align*} - 2 b^{\frac{3}{2}} x \left (\frac{1}{x}\right )^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12657, size = 16, normalized size = 1.33 \begin{align*} -\frac{2 \, b^{2} \mathrm{sgn}\left (x\right )}{\sqrt{b x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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