Optimal. Leaf size=20 \[ -\frac {\sqrt {6 x-x^2}}{3 x} \]
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Rubi [A] time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {650} \begin {gather*} -\frac {\sqrt {6 x-x^2}}{3 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 650
Rubi steps
\begin {align*} \int \frac {1}{x \sqrt {6 x-x^2}} \, dx &=-\frac {\sqrt {6 x-x^2}}{3 x}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.85 \begin {gather*} \frac {x-6}{3 \sqrt {-((x-6) x)}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.10, size = 20, normalized size = 1.00 \begin {gather*} -\frac {\sqrt {6 x-x^2}}{3 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 16, normalized size = 0.80 \begin {gather*} -\frac {\sqrt {-x^{2} + 6 \, x}}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.41, size = 25, normalized size = 1.25 \begin {gather*} \frac {2}{3 \, {\left (\frac {\sqrt {-x^{2} + 6 \, x} - 3}{x - 3} - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.85 \begin {gather*} \frac {x -6}{3 \sqrt {-x^{2}+6 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.43, size = 16, normalized size = 0.80 \begin {gather*} -\frac {\sqrt {-x^{2} + 6 \, x}}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.51, size = 16, normalized size = 0.80 \begin {gather*} -\frac {\sqrt {6\,x-x^2}}{3\,x} \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}{x \sqrt {- x \left (x - 6\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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