Optimal. Leaf size=13 \[ \frac {x \log (x)}{\sqrt {b x^2}} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {x \log (x)}{\sqrt {b x^2}} \end {gather*}
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*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {x \log (x)}{\sqrt {b x^2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.00, size = 18, normalized size = 1.38 \begin {gather*} \frac {\sqrt {b x^2} \log (x)}{b x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 16, normalized size = 1.23 \begin {gather*} \frac {\sqrt {b x^{2}} \log \relax (x)}{b x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 19, normalized size = 1.46 \begin {gather*} \frac {\log \left (\sqrt {{\left | b \right |}} {\left | x \right |} {\left | \mathrm {sgn}\relax (x) \right |}\right )}{\sqrt {b} \mathrm {sgn}\relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.92 \begin {gather*} \frac {x \ln \relax (x )}{\sqrt {b \,x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 6, normalized size = 0.46 \begin {gather*} \frac {\log \relax (x)}{\sqrt {b}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 10, normalized size = 0.77 \begin {gather*} \frac {\ln \left (b\,x\right )\,\mathrm {sign}\relax (x)}{\sqrt {b}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt {b x^{2}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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