Optimal. Leaf size=41 \[ \frac{1}{3} \left (x-\sqrt{x^2-4}\right )^{3/2}+\frac{4}{\sqrt{x-\sqrt{x^2-4}}} \]
[Out]
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Rubi [A] time = 0.0319785, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{1}{3} \left (x-\sqrt{x^2-4}\right )^{3/2}+\frac{4}{\sqrt{x-\sqrt{x^2-4}}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x - Sqrt[-4 + x^2]],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x - \sqrt{x^{2} - 4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x-(x**2-4)**(1/2))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0244141, size = 34, normalized size = 0.83 \[ \frac{2}{3} \sqrt{x-\sqrt{x^2-4}} \left (\sqrt{x^2-4}+2 x\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x - Sqrt[-4 + x^2]],x]
[Out]
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Maple [F] time = 0.051, size = 0, normalized size = 0. \[ \int \sqrt{x-\sqrt{{x}^{2}-4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x-(x^2-4)^(1/2))^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x - \sqrt{x^{2} - 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x - sqrt(x^2 - 4)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.280239, size = 41, normalized size = 1. \[ \frac{2 \,{\left (x^{2} - \sqrt{x^{2} - 4} x + 4\right )}}{3 \, \sqrt{x - \sqrt{x^{2} - 4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x - sqrt(x^2 - 4)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.902583, size = 42, normalized size = 1.02 \[ \frac{4 x \sqrt{x - \sqrt{x^{2} - 4}}}{3} + \frac{2 \sqrt{x - \sqrt{x^{2} - 4}} \sqrt{x^{2} - 4}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x-(x**2-4)**(1/2))**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x - \sqrt{x^{2} - 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x - sqrt(x^2 - 4)),x, algorithm="giac")
[Out]