Optimal. Leaf size=13 \[ \frac{x \log (x)}{\sqrt{b x^2}} \]
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Rubi [A] time = 0.0011591, 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} \[ \frac{x \log (x)}{\sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 29
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{b x^2}} \, dx &=\frac{x \int \frac{1}{x} \, dx}{\sqrt{b x^2}}\\ &=\frac{x \log (x)}{\sqrt{b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0001342, size = 13, normalized size = 1. \[ \frac{x \log (x)}{\sqrt{b x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 12, normalized size = 0.9 \begin{align*}{x\ln \left ( x \right ){\frac{1}{\sqrt{b{x}^{2}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.973724, size = 8, normalized size = 0.62 \begin{align*} \frac{\log \left (x\right )}{\sqrt{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45449, size = 35, normalized size = 2.69 \begin{align*} \frac{\sqrt{b x^{2}} \log \left (x\right )}{b x} \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 \frac{1}{\sqrt{b x^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.41165, size = 26, normalized size = 2. \begin{align*} \frac{\log \left (\sqrt{{\left | b \right |}}{\left | x \right |}{\left | \mathrm{sgn}\left (x\right ) \right |}\right )}{\sqrt{b} \mathrm{sgn}\left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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