Optimal. Leaf size=10 \[ -\sin ^{-1}\left (1-\frac {x}{3}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {619, 216} \[ -\sin ^{-1}\left (1-\frac {x}{3}\right ) \]
Antiderivative was successfully verified.
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Rule 216
Rule 619
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {6 x-x^2}} \, dx &=-\left (\frac {1}{6} \operatorname {Subst}\left (\int \frac {1}{\sqrt {1-\frac {x^2}{36}}} \, dx,x,6-2 x\right )\right )\\ &=-\sin ^{-1}\left (1-\frac {x}{3}\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.40 \[ -2 \sin ^{-1}\left (\sqrt {1-\frac {x}{6}}\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.60, size = 18, normalized size = 1.80 \[ -2 \, \arctan \left (\frac {\sqrt {-x^{2} + 6 \, x}}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 6, normalized size = 0.60 \[ \arcsin \left (\frac {1}{3} \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 7, normalized size = 0.70 \[ \arcsin \left (\frac {x}{3}-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 3.03, size = 8, normalized size = 0.80 \[ -\arcsin \left (-\frac {1}{3} \, x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 6, normalized size = 0.60 \[ \mathrm {asin}\left (\frac {x}{3}-1\right ) \]
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 \[ \int \frac {1}{\sqrt {- x^{2} + 6 x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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