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 = {664}
\begin {gather*} -\frac {\sqrt {6 x-x^2}}{3 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 664
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 {-6+x}{3 \sqrt {-((-6+x) x)}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.23, size = 17, normalized size = 0.85
method | result | size |
risch | \(\frac {-6+x}{3 \sqrt {-x \left (-6+x \right )}}\) | \(14\) |
gosper | \(\frac {-6+x}{3 \sqrt {-x^{2}+6 x}}\) | \(17\) |
default | \(-\frac {\sqrt {-x^{2}+6 x}}{3 x}\) | \(17\) |
trager | \(-\frac {\sqrt {-x^{2}+6 x}}{3 x}\) | \(17\) |
meijerg | \(-\frac {\sqrt {2}\, \sqrt {3}\, \sqrt {1-\frac {x}{6}}}{3 \sqrt {x}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.49, 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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Fricas [A]
time = 0.36, 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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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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Giac [A]
time = 4.96, 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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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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