Optimal. Leaf size=8 \[ -\sin ^{-1}(1-2 x) \]
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Rubi [A] time = 0.0049172, antiderivative size = 8, normalized size of antiderivative = 1., 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 1979
Rule 619
Rule 216
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*}
Mathematica [A] time = 0.0076131, size = 12, normalized size = 1.5 \[ -2 \sin ^{-1}\left (\sqrt{1-x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 7, normalized size = 0.9 \begin{align*} \arcsin \left ( 2\,x-1 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.54528, size = 8, normalized size = 1. \begin{align*} \arcsin \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.4491, size = 39, normalized size = 4.88 \begin{align*} -2 \, \arctan \left (\frac{\sqrt{-x^{2} + x}}{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{x \left (1 - x\right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20982, size = 8, normalized size = 1. \begin{align*} \arcsin \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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