Optimal. Leaf size=14 \[ -2 \operatorname {EllipticF}\left (\sin ^{-1}\left (\sqrt {4-x}\right ),-1\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, 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 221
Rule 689
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*}
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Mathematica [C] time = 0.02, size = 28, normalized size = 2.00 \[ -2 \sqrt {4-x} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};(4-x)^2\right ) \]
Antiderivative was successfully verified.
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fricas [F] time = 0.77, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {-x^{2} + 8 \, x - 15} \sqrt {-x + 4}}{x^{3} - 12 \, x^{2} + 47 \, x - 60}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {-x^{2} + 8 \, x - 15} \sqrt {-x + 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 47, normalized size = 3.36 \[ \frac {2 \sqrt {x -3}\, \sqrt {-x +5}\, \sqrt {-x^{2}+8 x -15}\, \EllipticF \left (\sqrt {-x +4}, i\right )}{x^{2}-8 x +15} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {-x^{2} + 8 \, x - 15} \sqrt {-x + 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {1}{\sqrt {4-x}\,\sqrt {-x^2+8\,x-15}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {- \left (x - 5\right ) \left (x - 3\right )} \sqrt {4 - x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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