Optimal. Leaf size=14 \[ -2 \text{EllipticF}\left (\sin ^{-1}\left (\sqrt{4-x}\right ),-1\right ) \]
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Rubi [A] time = 0.0103052, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {689, 221} \[ -2 F\left (\left .\sin ^{-1}\left (\sqrt{4-x}\right )\right |-1\right ) \]
Antiderivative was successfully verified.
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Rule 689
Rule 221
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{4-x} \sqrt{-15+8 x-x^2}} \, dx &=-\left (2 \operatorname{Subst}\left (\int \frac{1}{\sqrt{1-x^4}} \, dx,x,\sqrt{4-x}\right )\right )\\ &=-2 F\left (\left .\sin ^{-1}\left (\sqrt{4-x}\right )\right |-1\right )\\ \end{align*}
Mathematica [C] time = 0.0082709, size = 28, normalized size = 2. \[ -2 \sqrt{4-x} \, _2F_1\left (\frac{1}{4},\frac{1}{2};\frac{5}{4};(4-x)^2\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.012, size = 47, normalized size = 3.4 \begin{align*} 2\,{\frac{{\it EllipticF} \left ( \sqrt{-x+4},i \right ) \sqrt{-3+x}\sqrt{5-x}\sqrt{-{x}^{2}+8\,x-15}}{{x}^{2}-8\,x+15}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{-x^{2} + 8 \, x - 15} \sqrt{-x + 4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\sqrt{-x^{2} + 8 \, x - 15} \sqrt{-x + 4}}{x^{3} - 12 \, x^{2} + 47 \, x - 60}, 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{- \left (x - 5\right ) \left (x - 3\right )} \sqrt{4 - x}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{-x^{2} + 8 \, x - 15} \sqrt{-x + 4}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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