Optimal. Leaf size=8 \[ -\sin ^{-1}(2-x) \]
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Rubi [A] time = 0.0052765, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {619, 216} \[ -\sin ^{-1}(2-x) \]
Antiderivative was successfully verified.
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Rule 619
Rule 216
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{-3+4 x-x^2}} \, dx &=-\left (\frac{1}{2} \operatorname{Subst}\left (\int \frac{1}{\sqrt{1-\frac{x^2}{4}}} \, dx,x,4-2 x\right )\right )\\ &=-\sin ^{-1}(2-x)\\ \end{align*}
Mathematica [A] time = 0.0059099, size = 8, normalized size = 1. \[ -\sin ^{-1}(2-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 5, normalized size = 0.6 \begin{align*} \arcsin \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.4172, size = 11, normalized size = 1.38 \begin{align*} -\arcsin \left (-x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.79128, size = 74, normalized size = 9.25 \begin{align*} -\arctan \left (\frac{\sqrt{-x^{2} + 4 \, x - 3}{\left (x - 2\right )}}{x^{2} - 4 \, x + 3}\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} + 4 x - 3}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05988, size = 5, normalized size = 0.62 \begin{align*} \arcsin \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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