Optimal. Leaf size=33 \[ -\frac{\tan ^{-1}\left (\frac{2-3 x}{\sqrt{3} \sqrt{-3 x^2+4 x-2}}\right )}{\sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0203906, antiderivative size = 33, 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 \[ -\frac{\tan ^{-1}\left (\frac{2-3 x}{\sqrt{3} \sqrt{-3 x^2+4 x-2}}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[-2 + 4*x - 3*x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.48579, size = 34, normalized size = 1.03 \[ - \frac{\sqrt{3} \operatorname{atan}{\left (\frac{\sqrt{3} \left (- 6 x + 4\right )}{6 \sqrt{- 3 x^{2} + 4 x - 2}} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-3*x**2+4*x-2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0224558, size = 28, normalized size = 0.85 \[ -\frac{\tan ^{-1}\left (\frac{2-3 x}{\sqrt{-9 x^2+12 x-6}}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[-2 + 4*x - 3*x^2],x]
[Out]
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Maple [A] time = 0.003, size = 26, normalized size = 0.8 \[{\frac{\sqrt{3}}{3}\arctan \left ({\sqrt{3} \left ( x-{\frac{2}{3}} \right ){\frac{1}{\sqrt{-3\,{x}^{2}+4\,x-2}}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-3*x^2+4*x-2)^(1/2),x)
[Out]
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Maxima [A] time = 0.796606, size = 22, normalized size = 0.67 \[ -\frac{1}{3} i \, \sqrt{3} \operatorname{arsinh}\left (\frac{1}{2} \, \sqrt{2}{\left (3 \, x - 2\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-3*x^2 + 4*x - 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223021, size = 86, normalized size = 2.61 \[ \frac{1}{6} \, \sqrt{3}{\left (-i \, \log \left (\frac{2 i \, \sqrt{3} \sqrt{-3 \, x^{2} + 4 \, x - 2} - 6 \, x + 4}{x}\right ) + i \, \log \left (\frac{-2 i \, \sqrt{3} \sqrt{-3 \, x^{2} + 4 \, x - 2} - 6 \, x + 4}{x}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-3*x^2 + 4*x - 2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- 3 x^{2} + 4 x - 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-3*x**2+4*x-2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215377, size = 24, normalized size = 0.73 \[ -\frac{1}{3} \, \sqrt{3} i \arcsin \left (\frac{1}{2} \, \sqrt{2} i{\left (3 \, x - 2\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-3*x^2 + 4*x - 2),x, algorithm="giac")
[Out]