Optimal. Leaf size=13 \[ \sqrt {\frac {b}{x^2}} x \log (x) \]
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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*} x \sqrt {\frac {b}{x^2}} \log (x) \end {gather*}
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*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \sqrt {\frac {b}{x^2}} x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 12, normalized size = 0.92
method | result | size |
default | \(x \ln \left (x \right ) \sqrt {\frac {b}{x^{2}}}\) | \(12\) |
risch | \(x \ln \left (x \right ) \sqrt {\frac {b}{x^{2}}}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 11, normalized size = 0.85 \begin {gather*} x \sqrt {\frac {b}{x^{2}}} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 11, normalized size = 0.85 \begin {gather*} x \sqrt {\frac {b}{x^{2}}} \log \left (x\right ) \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 \sqrt {\frac {b}{x^{2}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.95, size = 9, normalized size = 0.69 \begin {gather*} \sqrt {b} \log \left ({\left | x \right |}\right ) \mathrm {sgn}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int \sqrt {\frac {b}{x^2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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