Optimal. Leaf size=16 \[ 2 \operatorname {EllipticF}\left (\sin ^{-1}\left (\frac {\sqrt {x-2}}{2}\right ),-4\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {119} \[ 2 F\left (\left .\sin ^{-1}\left (\frac {\sqrt {x-2}}{2}\right )\right |-4\right ) \]
Antiderivative was successfully verified.
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Rule 119
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {6-x} \sqrt {-2+x} \sqrt {-1+x}} \, dx &=2 F\left (\left .\sin ^{-1}\left (\frac {\sqrt {-2+x}}{2}\right )\right |-4\right )\\ \end {align*}
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Mathematica [C] time = 0.08, size = 74, normalized size = 4.62 \[ \frac {i \sqrt {\frac {4}{x-6}+1} \sqrt {\frac {5}{x-6}+1} (x-6)^{3/2} \operatorname {EllipticF}\left (i \sinh ^{-1}\left (\frac {2}{\sqrt {x-6}}\right ),\frac {5}{4}\right )}{\sqrt {-((x-6) (x-2))} \sqrt {x-1}} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.76, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\sqrt {x - 1} \sqrt {x - 2} \sqrt {-x + 6}}{x^{3} - 9 \, x^{2} + 20 \, x - 12}, x\right ) \]
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 \[ \int \frac {1}{\sqrt {x - 1} \sqrt {x - 2} \sqrt {-x + 6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 1.31 \[ -\frac {2 \sqrt {5}\, \EllipticF \left (\frac {\sqrt {-x +6}}{2}, \frac {2 \sqrt {5}}{5}\right )}{5} \]
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 \[ \int \frac {1}{\sqrt {x - 1} \sqrt {x - 2} \sqrt {-x + 6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {1}{\sqrt {x-1}\,\sqrt {x-2}\,\sqrt {6-x}} \,d x \]
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 \[ \int \frac {1}{\sqrt {6 - x} \sqrt {x - 2} \sqrt {x - 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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