Optimal. Leaf size=9 \[ 2 \sqrt{x+1} \]
[Out]
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Rubi [A] time = 0.00546179, antiderivative size = 9, 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 \[ 2 \sqrt{x+1} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - x]/Sqrt[1 - x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.40581, size = 7, normalized size = 0.78 \[ 2 \sqrt{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-x)**(1/2)/(-x**2+1)**(1/2),x)
[Out]
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Mathematica [B] time = 0.0125821, size = 25, normalized size = 2.78 \[ \frac{2 \sqrt{1-x} (x+1)}{\sqrt{1-x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - x]/Sqrt[1 - x^2],x]
[Out]
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Maple [B] time = 0.003, size = 22, normalized size = 2.4 \[ 2\,{\frac{ \left ( 1+x \right ) \sqrt{1-x}}{\sqrt{-{x}^{2}+1}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-x)^(1/2)/(-x^2+1)^(1/2),x)
[Out]
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Maxima [A] time = 0.688524, size = 9, normalized size = 1. \[ 2 \, \sqrt{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x + 1)/sqrt(-x^2 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.267257, size = 31, normalized size = 3.44 \[ -\frac{2 \,{\left (x^{2} - 1\right )}}{\sqrt{-x^{2} + 1} \sqrt{-x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x + 1)/sqrt(-x^2 + 1),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- x + 1}}{\sqrt{- \left (x - 1\right ) \left (x + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-x)**(1/2)/(-x**2+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.264204, size = 18, normalized size = 2. \[ -2 \, \sqrt{2} + 2 \, \sqrt{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x + 1)/sqrt(-x^2 + 1),x, algorithm="giac")
[Out]