Optimal. Leaf size=8 \[ -\sin ^{-1}(1-2 x) \]
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Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.273, Rules used = {1979, 619, 216} \[ -\sin ^{-1}(1-2 x) \]
Antiderivative was successfully verified.
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Rule 216
Rule 619
Rule 1979
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {(1-x) x}} \, dx &=\int \frac {1}{\sqrt {x-x^2}} \, dx\\ &=-\operatorname {Subst}\left (\int \frac {1}{\sqrt {1-x^2}} \, dx,x,1-2 x\right )\\ &=-\sin ^{-1}(1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.50 \[ -2 \sin ^{-1}\left (\sqrt {1-x}\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.45, size = 16, normalized size = 2.00 \[ -2 \, \arctan \left (\frac {\sqrt {-x^{2} + x}}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.39, size = 6, normalized size = 0.75 \[ \arcsin \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 7, normalized size = 0.88 \[ \arcsin \left (2 x -1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.96, size = 6, normalized size = 0.75 \[ \arcsin \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.01, size = 6, normalized size = 0.75 \[ \mathrm {asin}\left (2\,x-1\right ) \]
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 \[ \int \frac {1}{\sqrt {x \left (1 - x\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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