Optimal. Leaf size=24 \[ -\sqrt{2 x-x^2}-2 \sin ^{-1}(1-x) \]
[Out]
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Rubi [A] time = 0.024367, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ -\sqrt{2 x-x^2}-2 \sin ^{-1}(1-x) \]
Antiderivative was successfully verified.
[In] Int[(1 + x)/Sqrt[2*x - x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.90138, size = 15, normalized size = 0.62 \[ - \sqrt{- x^{2} + 2 x} + 2 \operatorname{asin}{\left (x - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+x)/(-x**2+2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0270264, size = 45, normalized size = 1.88 \[ \frac{(x-2) x+4 \sqrt{x-2} \sqrt{x} \log \left (\sqrt{x-2}+\sqrt{x}\right )}{\sqrt{-(x-2) x}} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x)/Sqrt[2*x - x^2],x]
[Out]
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Maple [A] time = 0.008, size = 21, normalized size = 0.9 \[ 2\,\arcsin \left ( -1+x \right ) -\sqrt{-{x}^{2}+2\,x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+x)/(-x^2+2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.50315, size = 30, normalized size = 1.25 \[ -\sqrt{-x^{2} + 2 \, x} - 2 \, \arcsin \left (-x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/sqrt(-x^2 + 2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247878, size = 43, normalized size = 1.79 \[ -\sqrt{-x^{2} + 2 \, x} - 4 \, \arctan \left (\frac{\sqrt{-x^{2} + 2 \, x}}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/sqrt(-x^2 + 2*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x + 1}{\sqrt{- x \left (x - 2\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+x)/(-x**2+2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212486, size = 27, normalized size = 1.12 \[ -\sqrt{-x^{2} + 2 \, x} + 2 \, \arcsin \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 1)/sqrt(-x^2 + 2*x),x, algorithm="giac")
[Out]