Optimal. Leaf size=27 \[ \sin ^{-1}\left (\frac{1}{2} (-x-1)\right )-\sqrt{-x^2-2 x+3} \]
[Out]
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Rubi [A] time = 0.0264479, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ \sin ^{-1}\left (\frac{1}{2} (-x-1)\right )-\sqrt{-x^2-2 x+3} \]
Antiderivative was successfully verified.
[In] Int[x/Sqrt[3 - 2*x - x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.91482, size = 36, normalized size = 1.33 \[ - \sqrt{- x^{2} - 2 x + 3} - \operatorname{atan}{\left (- \frac{- 2 x - 2}{2 \sqrt{- x^{2} - 2 x + 3}} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(-x**2-2*x+3)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0166762, size = 27, normalized size = 1. \[ \sin ^{-1}\left (\frac{1}{2} (-x-1)\right )-\sqrt{-x^2-2 x+3} \]
Antiderivative was successfully verified.
[In] Integrate[x/Sqrt[3 - 2*x - x^2],x]
[Out]
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Maple [A] time = 0.007, size = 24, normalized size = 0.9 \[ -\arcsin \left ({\frac{1}{2}}+{\frac{x}{2}} \right ) -\sqrt{-{x}^{2}-2\,x+3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(-x^2-2*x+3)^(1/2),x)
[Out]
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Maxima [A] time = 1.54533, size = 28, normalized size = 1.04 \[ -\sqrt{-x^{2} - 2 \, x + 3} + \arcsin \left (-\frac{1}{2} \, x - \frac{1}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(-x^2 - 2*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216014, size = 46, normalized size = 1.7 \[ -\sqrt{-x^{2} - 2 \, x + 3} - \arctan \left (\frac{x + 1}{\sqrt{-x^{2} - 2 \, x + 3}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(-x^2 - 2*x + 3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{\sqrt{- \left (x - 1\right ) \left (x + 3\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x**2-2*x+3)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.206193, size = 31, normalized size = 1.15 \[ -\sqrt{-x^{2} - 2 \, x + 3} - \arcsin \left (\frac{1}{2} \, x + \frac{1}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(-x^2 - 2*x + 3),x, algorithm="giac")
[Out]