Optimal. Leaf size=17 \[ -\frac{b \sqrt{\frac{b}{x^2}}}{2 x} \]
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Rubi [A] time = 0.0017096, 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} \[ -\frac{b \sqrt{\frac{b}{x^2}}}{2 x} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \left (\frac{b}{x^2}\right )^{3/2} \, dx &=\left (b \sqrt{\frac{b}{x^2}} x\right ) \int \frac{1}{x^3} \, dx\\ &=-\frac{b \sqrt{\frac{b}{x^2}}}{2 x}\\ \end{align*}
Mathematica [A] time = 0.0012056, size = 14, normalized size = 0.82 \[ -\frac{1}{2} x \left (\frac{b}{x^2}\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.7 \begin{align*} -{\frac{x}{2} \left ({\frac{b}{{x}^{2}}} \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.982693, size = 14, normalized size = 0.82 \begin{align*} -\frac{1}{2} \, x \left (\frac{b}{x^{2}}\right )^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73148, size = 30, normalized size = 1.76 \begin{align*} -\frac{b \sqrt{\frac{b}{x^{2}}}}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.70477, size = 17, normalized size = 1. \begin{align*} - \frac{b^{\frac{3}{2}} x \left (\frac{1}{x^{2}}\right )^{\frac{3}{2}}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12262, size = 14, normalized size = 0.82 \begin{align*} -\frac{b^{\frac{3}{2}} \mathrm{sgn}\left (x\right )}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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