Optimal. Leaf size=17 \[ \frac{\sqrt{x+1}}{\sqrt{1-x}} \]
[Out]
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Rubi [A] time = 0.0156638, antiderivative size = 17, 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 \[ \frac{\sqrt{x+1}}{\sqrt{1-x}} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - x)^(3/2)*Sqrt[1 + x]),x]
[Out]
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Rubi in Sympy [A] time = 2.37912, size = 12, normalized size = 0.71 \[ \frac{\sqrt{x + 1}}{\sqrt{- x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-x)**(3/2)/(1+x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0129875, size = 19, normalized size = 1.12 \[ \frac{\sqrt{1-x^2}}{1-x} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - x)^(3/2)*Sqrt[1 + x]),x]
[Out]
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Maple [A] time = 0.006, size = 14, 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)^(3/2)/(1+x)^(1/2),x)
[Out]
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Maxima [A] time = 1.499, size = 22, normalized size = 1.29 \[ -\frac{\sqrt{-x^{2} + 1}}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 1)*(-x + 1)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204786, size = 28, normalized size = 1.65 \[ \frac{2 \, x}{x + \sqrt{x + 1} \sqrt{-x + 1} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 1)*(-x + 1)^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.61606, size = 31, normalized size = 1.82 \[ \begin{cases} \frac{1}{\sqrt{-1 + \frac{2}{x + 1}}} & \text{for}\: 2 \left |{\frac{1}{x + 1}}\right | > 1 \\- \frac{i}{\sqrt{1 - \frac{2}{x + 1}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-x)**(3/2)/(1+x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.207985, size = 26, normalized size = 1.53 \[ -\frac{\sqrt{x + 1} \sqrt{-x + 1}}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 1)*(-x + 1)^(3/2)),x, algorithm="giac")
[Out]