Optimal. Leaf size=46 \[ -\frac{1}{2} \sqrt{2 x-x^2} x-\frac{3}{2} \sqrt{2 x-x^2}-\frac{3}{2} \sin ^{-1}(1-x) \]
[Out]
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Rubi [A] time = 0.0533722, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.235 \[ -\frac{1}{2} \sqrt{2 x-x^2} x-\frac{3}{2} \sqrt{2 x-x^2}-\frac{3}{2} \sin ^{-1}(1-x) \]
Antiderivative was successfully verified.
[In] Int[x^2/Sqrt[2*x - x^2],x]
[Out]
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Rubi in Sympy [A] time = 5.51362, size = 34, normalized size = 0.74 \[ - \frac{x \sqrt{- x^{2} + 2 x}}{2} - \frac{3 \sqrt{- x^{2} + 2 x}}{2} + \frac{3 \operatorname{asin}{\left (x - 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(-x**2+2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0310124, size = 51, normalized size = 1.11 \[ \frac{x \left (x^2+x-6\right )+6 \sqrt{x-2} \sqrt{x} \log \left (\sqrt{x-2}+\sqrt{x}\right )}{2 \sqrt{-(x-2) x}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/Sqrt[2*x - x^2],x]
[Out]
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Maple [A] time = 0.006, size = 35, normalized size = 0.8 \[{\frac{3\,\arcsin \left ( -1+x \right ) }{2}}-{\frac{3}{2}\sqrt{-{x}^{2}+2\,x}}-{\frac{x}{2}\sqrt{-{x}^{2}+2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(-x^2+2*x)^(1/2),x)
[Out]
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Maxima [A] time = 0.784022, size = 49, normalized size = 1.07 \[ -\frac{1}{2} \, \sqrt{-x^{2} + 2 \, x} x - \frac{3}{2} \, \sqrt{-x^{2} + 2 \, x} - \frac{3}{2} \, \arcsin \left (-x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(-x^2 + 2*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232911, size = 47, normalized size = 1.02 \[ -\frac{1}{2} \, \sqrt{-x^{2} + 2 \, x}{\left (x + 3\right )} - 3 \, \arctan \left (\frac{\sqrt{-x^{2} + 2 \, x}}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(-x^2 + 2*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2}}{\sqrt{- x \left (x - 2\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(-x**2+2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213876, size = 31, normalized size = 0.67 \[ -\frac{1}{2} \, \sqrt{-x^{2} + 2 \, x}{\left (x + 3\right )} + \frac{3}{2} \, \arcsin \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/sqrt(-x^2 + 2*x),x, algorithm="giac")
[Out]