Optimal. Leaf size=13 \[ \tan ^{-1}\left (\sqrt{x^2-4 x+3}\right ) \]
[Out]
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Rubi [A] time = 0.0266645, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \tan ^{-1}\left (\sqrt{x^2-4 x+3}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/((-2 + x)*Sqrt[3 - 4*x + x^2]),x]
[Out]
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Rubi in Sympy [A] time = 5.51505, size = 12, normalized size = 0.92 \[ \operatorname{atan}{\left (\sqrt{x^{2} - 4 x + 3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-2+x)/(x**2-4*x+3)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0121926, size = 14, normalized size = 1.08 \[ -\tan ^{-1}\left (\frac{1}{\sqrt{(x-2)^2-1}}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/((-2 + x)*Sqrt[3 - 4*x + x^2]),x]
[Out]
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Maple [A] time = 0.008, size = 13, normalized size = 1. \[ -\arctan \left ({\frac{1}{\sqrt{ \left ( x-2 \right ) ^{2}-1}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x-2)/(x^2-4*x+3)^(1/2),x)
[Out]
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Maxima [A] time = 0.746995, size = 12, normalized size = 0.92 \[ -\arcsin \left (\frac{1}{{\left | x - 2 \right |}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 - 4*x + 3)*(x - 2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219727, size = 24, normalized size = 1.85 \[ 2 \, \arctan \left (-x + \sqrt{x^{2} - 4 \, x + 3} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 - 4*x + 3)*(x - 2)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{\left (x - 3\right ) \left (x - 1\right )} \left (x - 2\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-2+x)/(x**2-4*x+3)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.207598, size = 24, normalized size = 1.85 \[ 2 \, \arctan \left (-x + \sqrt{x^{2} - 4 \, x + 3} + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 - 4*x + 3)*(x - 2)),x, algorithm="giac")
[Out]