Optimal. Leaf size=12 \[ -\sin ^{-1}\left (\frac{1}{3} (1-2 x)\right ) \]
[Out]
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Rubi [A] time = 0.0138181, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ -\sin ^{-1}\left (\frac{1}{3} (1-2 x)\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[2 + x - x^2],x]
[Out]
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Rubi in Sympy [A] time = 0.665824, size = 19, normalized size = 1.58 \[ - \operatorname{atan}{\left (\frac{- 2 x + 1}{2 \sqrt{- x^{2} + x + 2}} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-x**2+x+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0087237, size = 12, normalized size = 1. \[ -\sin ^{-1}\left (\frac{1}{3} (1-2 x)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[2 + x - x^2],x]
[Out]
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Maple [A] time = 0.006, size = 7, normalized size = 0.6 \[ \arcsin \left ( -{\frac{1}{3}}+{\frac{2\,x}{3}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-x^2+x+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.52782, size = 11, normalized size = 0.92 \[ -\arcsin \left (-\frac{2}{3} \, x + \frac{1}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^2 + x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213481, size = 24, normalized size = 2. \[ \arctan \left (\frac{2 \, x - 1}{2 \, \sqrt{-x^{2} + x + 2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^2 + x + 2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- x^{2} + x + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-x**2+x+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212079, size = 8, normalized size = 0.67 \[ \arcsin \left (\frac{2}{3} \, x - \frac{1}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^2 + x + 2),x, algorithm="giac")
[Out]