Optimal. Leaf size=14 \[ \frac{x}{2 \sqrt{\frac{b}{x^2}}} \]
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Rubi [A] time = 0.0014358, 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} \[ \frac{x}{2 \sqrt{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{\frac{b}{x^2}}} \, dx &=\frac{\int x \, dx}{\sqrt{\frac{b}{x^2}} x}\\ &=\frac{x}{2 \sqrt{\frac{b}{x^2}}}\\ \end{align*}
Mathematica [A] time = 0.0016363, size = 14, normalized size = 1. \[ \frac{x}{2 \sqrt{\frac{b}{x^2}}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.8 \begin{align*}{\frac{x}{2}{\frac{1}{\sqrt{{\frac{b}{{x}^{2}}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00709, size = 14, normalized size = 1. \begin{align*} \frac{x}{2 \, \sqrt{\frac{b}{x^{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72275, size = 31, normalized size = 2.21 \begin{align*} \frac{x^{3} \sqrt{\frac{b}{x^{2}}}}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.463038, size = 15, normalized size = 1.07 \begin{align*} \frac{x}{2 \sqrt{b} \sqrt{\frac{1}{x^{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18242, size = 16, normalized size = 1.14 \begin{align*} \frac{x^{2}}{2 \, \sqrt{b} \mathrm{sgn}\left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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