Optimal. Leaf size=25 \[ -\frac {2 \operatorname {EllipticF}\left (\sin ^{-1}\left (\frac {\sqrt {6-x}}{2}\right ),\frac {4}{5}\right )}{\sqrt {5}} \]
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Rubi [A] time = 0.02, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {718, 419} \[ -\frac {2 F\left (\sin ^{-1}\left (\frac {\sqrt {6-x}}{2}\right )|\frac {4}{5}\right )}{\sqrt {5}} \]
Antiderivative was successfully verified.
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Rule 419
Rule 718
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {-1+x} \sqrt {-12+8 x-x^2}} \, dx &=-\frac {2 \operatorname {Subst}\left (\int \frac {1}{\sqrt {1-x^2} \sqrt {1-\frac {4 x^2}{5}}} \, dx,x,\frac {\sqrt {12-2 x}}{2 \sqrt {2}}\right )}{\sqrt {5}}\\ &=-\frac {2 F\left (\sin ^{-1}\left (\frac {\sqrt {6-x}}{2}\right )|\frac {4}{5}\right )}{\sqrt {5}}\\ \end {align*}
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Mathematica [B] time = 0.10, size = 68, normalized size = 2.72 \[ -\frac {2 \sqrt {\frac {x-6}{x-1}} \sqrt {\frac {x-2}{x-1}} (x-1) \operatorname {EllipticF}\left (\sin ^{-1}\left (\frac {\sqrt {5}}{\sqrt {x-1}}\right ),\frac {1}{5}\right )}{\sqrt {5} \sqrt {-x^2+8 x-12}} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.58, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\sqrt {-x^{2} + 8 \, x - 12} \sqrt {x - 1}}{x^{3} - 9 \, x^{2} + 20 \, x - 12}, x\right ) \]
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 \[ \int \frac {1}{\sqrt {-x^{2} + 8 \, x - 12} \sqrt {x - 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 55, normalized size = 2.20 \[ \frac {2 \sqrt {x -2}\, \sqrt {5}\, \sqrt {-x +6}\, \sqrt {-x^{2}+8 x -12}\, \EllipticF \left (\frac {\sqrt {-x +6}}{2}, \frac {2 \sqrt {5}}{5}\right )}{5 \left (x^{2}-8 x +12\right )} \]
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 \[ \int \frac {1}{\sqrt {-x^{2} + 8 \, x - 12} \sqrt {x - 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{\sqrt {x-1}\,\sqrt {-x^2+8\,x-12}} \,d x \]
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 \[ \int \frac {1}{\sqrt {- \left (x - 6\right ) \left (x - 2\right )} \sqrt {x - 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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