Optimal. Leaf size=8 \[ -\sin ^{-1}(5-2 x) \]
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Rubi [A] time = 0.0041647, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176, Rules used = {53, 619, 216} \[ -\sin ^{-1}(5-2 x) \]
Antiderivative was successfully verified.
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Rule 53
Rule 619
Rule 216
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{3-x} \sqrt{-2+x}} \, dx &=\int \frac{1}{\sqrt{-6+5 x-x^2}} \, dx\\ &=-\operatorname{Subst}\left (\int \frac{1}{\sqrt{1-x^2}} \, dx,x,5-2 x\right )\\ &=-\sin ^{-1}(5-2 x)\\ \end{align*}
Mathematica [A] time = 0.0100673, size = 12, normalized size = 1.5 \[ -2 \sin ^{-1}\left (\sqrt{3-x}\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.003, size = 31, normalized size = 3.9 \begin{align*}{\arcsin \left ( 2\,x-5 \right ) \sqrt{ \left ( -2+x \right ) \left ( 3-x \right ) }{\frac{1}{\sqrt{3-x}}}{\frac{1}{\sqrt{-2+x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.48708, size = 8, normalized size = 1. \begin{align*} \arcsin \left (2 \, x - 5\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.58787, size = 88, normalized size = 11. \begin{align*} -\arctan \left (\frac{{\left (2 \, x - 5\right )} \sqrt{x - 2} \sqrt{-x + 3}}{2 \,{\left (x^{2} - 5 \, x + 6\right )}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.61958, size = 26, normalized size = 3.25 \begin{align*} \begin{cases} - 2 i \operatorname{acosh}{\left (\sqrt{x - 2} \right )} & \text{for}\: \left |{x - 2}\right | > 1 \\2 \operatorname{asin}{\left (\sqrt{x - 2} \right )} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08056, size = 11, normalized size = 1.38 \begin{align*} 2 \, \arcsin \left (\sqrt{x - 2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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