Optimal. Leaf size=14 \[ \frac{2 x}{5 \sqrt{\frac{b}{x^3}}} \]
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Rubi [A] time = 0.0014239, 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} \[ \frac{2 x}{5 \sqrt{\frac{b}{x^3}}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{\frac{b}{x^3}}} \, dx &=\frac{\int x^{3/2} \, dx}{\sqrt{\frac{b}{x^3}} x^{3/2}}\\ &=\frac{2 x}{5 \sqrt{\frac{b}{x^3}}}\\ \end{align*}
Mathematica [A] time = 0.0016246, size = 14, normalized size = 1. \[ \frac{2 x}{5 \sqrt{\frac{b}{x^3}}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.8 \begin{align*}{\frac{2\,x}{5}{\frac{1}{\sqrt{{\frac{b}{{x}^{3}}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955916, size = 14, normalized size = 1. \begin{align*} \frac{2 \, x}{5 \, \sqrt{\frac{b}{x^{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.69002, size = 31, normalized size = 2.21 \begin{align*} \frac{2 \, x^{4} \sqrt{\frac{b}{x^{3}}}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.39797, size = 17, normalized size = 1.21 \begin{align*} \frac{2 x}{5 \sqrt{b} \sqrt{\frac{1}{x^{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17394, size = 18, normalized size = 1.29 \begin{align*} \frac{2 \, \sqrt{b x} x^{2}}{5 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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