Optimal. Leaf size=8 \[ -\sin ^{-1}(5-2 x) \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\sin ^{-1}(5-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 53
Rule 216
Rule 619
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 = 0.01, size = 12, normalized size = 1.50 \begin {gather*} -2 \sin ^{-1}\left (\sqrt {3-x}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [B] time = 0.04, size = 20, normalized size = 2.50 \begin {gather*} -2 \tan ^{-1}\left (\frac {\sqrt {3-x}}{\sqrt {x-2}}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 1.35, size = 32, normalized size = 4.00 \begin {gather*} -\arctan \left (\frac {{\left (2 \, x - 5\right )} \sqrt {x - 2} \sqrt {-x + 3}}{2 \, {\left (x^{2} - 5 \, x + 6\right )}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.02, size = 8, normalized size = 1.00 \begin {gather*} 2 \, \arcsin \left (\sqrt {x - 2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.00, size = 31, normalized size = 3.88 \begin {gather*} \frac {\sqrt {\left (x -2\right ) \left (-x +3\right )}\, \arcsin \left (2 x -5\right )}{\sqrt {x -2}\, \sqrt {-x +3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 3.00, size = 6, normalized size = 0.75 \begin {gather*} \arcsin \left (2 \, x - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.18, size = 31, normalized size = 3.88 \begin {gather*} -4\,\mathrm {atan}\left (\frac {\sqrt {x-2}-\sqrt {2}\,1{}\mathrm {i}}{\sqrt {3}-\sqrt {3-x}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.61, size = 26, normalized size = 3.25 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________