Optimal. Leaf size=11 \[ \frac{2}{3} (x+1)^{3/2} \]
[Out]
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Rubi [A] time = 0.00532804, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ \frac{2}{3} (x+1)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - x^2]/Sqrt[1 - x],x]
[Out]
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Rubi in Sympy [A] time = 1.40369, size = 8, normalized size = 0.73 \[ \frac{2 \left (x + 1\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**2+1)**(1/2)/(1-x)**(1/2),x)
[Out]
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Mathematica [B] time = 0.0120282, size = 27, normalized size = 2.45 \[ \frac{2 (x+1) \sqrt{1-x^2}}{3 \sqrt{1-x}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - x^2]/Sqrt[1 - x],x]
[Out]
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Maple [B] time = 0.003, size = 22, normalized size = 2. \[{\frac{2+2\,x}{3}\sqrt{-{x}^{2}+1}{\frac{1}{\sqrt{1-x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^2+1)^(1/2)/(1-x)^(1/2),x)
[Out]
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Maxima [A] time = 0.69087, size = 9, normalized size = 0.82 \[ \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 1)/sqrt(-x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.263995, size = 39, normalized size = 3.55 \[ -\frac{2 \,{\left (x^{3} + x^{2} - x - 1\right )}}{3 \, \sqrt{-x^{2} + 1} \sqrt{-x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 1)/sqrt(-x + 1),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- \left (x - 1\right ) \left (x + 1\right )}}{\sqrt{- x + 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**2+1)**(1/2)/(1-x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.264834, size = 18, normalized size = 1.64 \[ \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} - \frac{4}{3} \, \sqrt{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 1)/sqrt(-x + 1),x, algorithm="giac")
[Out]