Optimal. Leaf size=13 \[ x \sqrt{\frac{b}{x^2}} \log (x) \]
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Rubi [A] time = 0.0025132, antiderivative size = 13, 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, 29} \[ x \sqrt{\frac{b}{x^2}} \log (x) \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin{align*} \int \sqrt{\frac{b}{x^2}} \, dx &=\left (\sqrt{\frac{b}{x^2}} x\right ) \int \frac{1}{x} \, dx\\ &=\sqrt{\frac{b}{x^2}} x \log (x)\\ \end{align*}
Mathematica [A] time = 0.0012014, size = 13, normalized size = 1. \[ x \sqrt{\frac{b}{x^2}} \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, normalized size = 0.9 \begin{align*} x\ln \left ( x \right ) \sqrt{{\frac{b}{{x}^{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.39201, size = 15, normalized size = 1.15 \begin{align*} x \sqrt{\frac{b}{x^{2}}} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68759, size = 30, normalized size = 2.31 \begin{align*} x \sqrt{\frac{b}{x^{2}}} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{\frac{b}{x^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1727, size = 12, normalized size = 0.92 \begin{align*} \sqrt{b} \log \left ({\left | x \right |}\right ) \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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