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 = 0.03, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {1982, 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
Rule 1982
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {(6-x) (-2+x)} \sqrt {-1+x}} \, dx &=\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 [C] time = 0.04, size = 74, normalized size = 2.96 \[ \frac {i \sqrt {\frac {4}{x-6}+1} \sqrt {\frac {5}{x-6}+1} (x-6)^{3/2} \operatorname {EllipticF}\left (i \sinh ^{-1}\left (\frac {2}{\sqrt {x-6}}\right ),\frac {5}{4}\right )}{\sqrt {-((x-6) (x-2))} \sqrt {x-1}} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.72, 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 \[ \int \frac {1}{\sqrt {-{\left (x - 2\right )} {\left (x - 6\right )}} \sqrt {x - 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 43, normalized size = 1.72 \[ -\frac {2 \sqrt {x -2}\, \sqrt {-x +6}\, \sqrt {5}\, \EllipticF \left (\frac {\sqrt {-x +6}}{2}, \frac {2 \sqrt {5}}{5}\right )}{5 \sqrt {-\left (x -2\right ) \left (x -6\right )}} \]
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 \[ \int \frac {1}{\sqrt {-{\left (x - 2\right )} {\left (x - 6\right )}} \sqrt {x - 1}}\,{d x} \]
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 \[ \int \frac {1}{\sqrt {-\left (x-2\right )\,\left (x-6\right )}\,\sqrt {x-1}} \,d x \]
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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