Optimal. Leaf size=18 \[ -\frac{\sqrt{1-x}}{\sqrt{x+1}} \]
[Out]
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Rubi [A] time = 0.011929, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{\sqrt{1-x}}{\sqrt{x+1}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 - x]*(1 + x)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 2.43945, size = 14, normalized size = 0.78 \[ - \frac{\sqrt{- x + 1}}{\sqrt{x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-x)**(1/2)/(1+x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00990987, size = 18, normalized size = 1. \[ -\frac{\sqrt{1-x}}{\sqrt{x+1}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 - x]*(1 + x)^(3/2)),x]
[Out]
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Maple [A] time = 0.004, size = 15, normalized size = 0.8 \[ -{1\sqrt{1-x}{\frac{1}{\sqrt{1+x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-x)^(1/2)/(1+x)^(3/2),x)
[Out]
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Maxima [A] time = 1.5101, size = 22, normalized size = 1.22 \[ -\frac{\sqrt{-x^{2} + 1}}{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 1)^(3/2)*sqrt(-x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203705, size = 30, normalized size = 1.67 \[ -\frac{2 \, x}{x - \sqrt{x + 1} \sqrt{-x + 1} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 1)^(3/2)*sqrt(-x + 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.89458, size = 31, normalized size = 1.72 \[ \begin{cases} - \sqrt{-1 + \frac{2}{x + 1}} & \text{for}\: 2 \left |{\frac{1}{x + 1}}\right | > 1 \\- i \sqrt{1 - \frac{2}{x + 1}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-x)**(1/2)/(1+x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.207629, size = 58, normalized size = 3.22 \[ \frac{\sqrt{2} - \sqrt{-x + 1}}{2 \, \sqrt{x + 1}} - \frac{\sqrt{x + 1}}{2 \,{\left (\sqrt{2} - \sqrt{-x + 1}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 1)^(3/2)*sqrt(-x + 1)),x, algorithm="giac")
[Out]