Optimal. Leaf size=10 \[ \frac{1}{2} \sin ^{-1}\left (x+\frac{1}{2}\right ) \]
[Out]
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Rubi [A] time = 0.0146968, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{1}{2} \sin ^{-1}\left (x+\frac{1}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[3 - 4*x - 4*x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.5281, size = 26, normalized size = 2.6 \[ \frac{\operatorname{atan}{\left (- \frac{- 8 x - 4}{4 \sqrt{- 4 x^{2} - 4 x + 3}} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-4*x**2-4*x+3)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0100993, size = 14, normalized size = 1.4 \[ -\frac{1}{2} \sin ^{-1}\left (\frac{1}{2} (-2 x-1)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[3 - 4*x - 4*x^2],x]
[Out]
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Maple [A] time = 0.003, size = 7, normalized size = 0.7 \[{\frac{1}{2}\arcsin \left ({\frac{1}{2}}+x \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-4*x^2-4*x+3)^(1/2),x)
[Out]
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Maxima [A] time = 0.804628, size = 11, normalized size = 1.1 \[ -\frac{1}{2} \, \arcsin \left (-x - \frac{1}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-4*x^2 - 4*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228652, size = 28, normalized size = 2.8 \[ \frac{1}{2} \, \arctan \left (\frac{2 \, x + 1}{\sqrt{-4 \, x^{2} - 4 \, x + 3}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-4*x^2 - 4*x + 3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- 4 x^{2} - 4 x + 3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-4*x**2-4*x+3)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.211983, size = 8, normalized size = 0.8 \[ \frac{1}{2} \, \arcsin \left (x + \frac{1}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-4*x^2 - 4*x + 3),x, algorithm="giac")
[Out]