Optimal. Leaf size=10 \[ -\sin ^{-1}\left (1-\frac{x}{3}\right ) \]
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Rubi [A] time = 0.0062504, antiderivative size = 10, normalized size of antiderivative = 1., 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 619
Rule 216
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*}
Mathematica [A] time = 0.0096672, size = 14, normalized size = 1.4 \[ -2 \sin ^{-1}\left (\sqrt{1-\frac{x}{6}}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.065, size = 7, normalized size = 0.7 \begin{align*} \arcsin \left ( -1+{\frac{x}{3}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 3.88425, size = 11, normalized size = 1.1 \begin{align*} -\arcsin \left (-\frac{1}{3} \, x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.27557, size = 42, normalized size = 4.2 \begin{align*} -2 \, \arctan \left (\frac{\sqrt{-x^{2} + 6 \, x}}{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{- x^{2} + 6 x}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.61726, size = 8, normalized size = 0.8 \begin{align*} \arcsin \left (\frac{1}{3} \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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