Optimal. Leaf size=12 \[ -2 x \sqrt{\frac{b}{x^3}} \]
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Rubi [A] time = 0.0016037, 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} \[ -2 x \sqrt{\frac{b}{x^3}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \sqrt{\frac{b}{x^3}} \, dx &=\left (\sqrt{\frac{b}{x^3}} x^{3/2}\right ) \int \frac{1}{x^{3/2}} \, dx\\ &=-2 \sqrt{\frac{b}{x^3}} x\\ \end{align*}
Mathematica [A] time = 0.0012782, size = 12, normalized size = 1. \[ -2 x \sqrt{\frac{b}{x^3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.9 \begin{align*} -2\,x\sqrt{{\frac{b}{{x}^{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96852, size = 14, normalized size = 1.17 \begin{align*} -2 \, x \sqrt{\frac{b}{x^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.64766, size = 24, normalized size = 2. \begin{align*} -2 \, x \sqrt{\frac{b}{x^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.41267, size = 17, normalized size = 1.42 \begin{align*} - 2 \sqrt{b} x \sqrt{\frac{1}{x^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14144, size = 11, normalized size = 0.92 \begin{align*} -\frac{2 \, b}{\sqrt{b x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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