Optimal. Leaf size=51 \[ -\frac{2 \sqrt{-x^2+3 x-1} F\left (\left .\sin ^{-1}\left (\frac{\sqrt{3-2 x}}{\sqrt [4]{5}}\right )\right |-1\right )}{\sqrt [4]{5} \sqrt{x^2-3 x+1}} \]
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Rubi [A] time = 0.0733167, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.136 \[ -\frac{2 \sqrt{-x^2+3 x-1} F\left (\left .\sin ^{-1}\left (\frac{\sqrt{3-2 x}}{\sqrt [4]{5}}\right )\right |-1\right )}{\sqrt [4]{5} \sqrt{x^2-3 x+1}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[3 - 2*x]*Sqrt[1 - 3*x + x^2]),x]
[Out]
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Rubi in Sympy [A] time = 10.019, size = 56, normalized size = 1.1 \[ - \frac{2 \sqrt [4]{5} \sqrt{- \frac{x^{2}}{5} + \frac{3 x}{5} - \frac{1}{5}} F\left (\operatorname{asin}{\left (\frac{5^{\frac{3}{4}} \sqrt{- 2 x + 3}}{5} \right )}\middle | -1\right )}{\sqrt{x^{2} - 3 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3-2*x)**(1/2)/(x**2-3*x+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0919378, size = 60, normalized size = 1.18 \[ \frac{2 \sqrt{(3-2 x)^2-5} F\left (\left .\sin ^{-1}\left (\frac{\sqrt [4]{5}}{\sqrt{3-2 x}}\right )\right |-1\right )}{\sqrt [4]{5} \sqrt{1-\frac{5}{(3-2 x)^2}} (3-2 x)} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[3 - 2*x]*Sqrt[1 - 3*x + x^2]),x]
[Out]
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Maple [B] time = 0.046, size = 102, normalized size = 2. \[{\frac{1}{10\,{x}^{3}-45\,{x}^{2}+55\,x-15}\sqrt{3-2\,x}\sqrt{{x}^{2}-3\,x+1}\sqrt{ \left ( -2\,x+3+\sqrt{5} \right ) \sqrt{5}}\sqrt{ \left ( -3+2\,x \right ) \sqrt{5}}\sqrt{ \left ( 2\,x-3+\sqrt{5} \right ) \sqrt{5}}{\it EllipticF} \left ({\frac{\sqrt{2}\sqrt{5}}{10}\sqrt{ \left ( -2\,x+3+\sqrt{5} \right ) \sqrt{5}}},\sqrt{2} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3-2*x)^(1/2)/(x^2-3*x+1)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x^{2} - 3 \, x + 1} \sqrt{-2 \, x + 3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 - 3*x + 1)*sqrt(-2*x + 3)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{x^{2} - 3 \, x + 1} \sqrt{-2 \, x + 3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 - 3*x + 1)*sqrt(-2*x + 3)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- 2 x + 3} \sqrt{x^{2} - 3 x + 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3-2*x)**(1/2)/(x**2-3*x+1)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x^{2} - 3 \, x + 1} \sqrt{-2 \, x + 3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 - 3*x + 1)*sqrt(-2*x + 3)),x, algorithm="giac")
[Out]