Optimal. Leaf size=20 \[ -\sqrt{\frac{1-x}{x+1}} (x+1) \]
[Out]
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Rubi [A] time = 0.0885777, antiderivative size = 20, 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 \[ -\sqrt{\frac{1-x}{x+1}} (x+1) \]
Antiderivative was successfully verified.
[In] Int[x/(Sqrt[(1 - x)/(1 + x)]*(1 + x)),x]
[Out]
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Rubi in Sympy [A] time = 3.94377, size = 20, normalized size = 1. \[ - \frac{2 \sqrt{\frac{- x + 1}{x + 1}}}{\frac{- x + 1}{x + 1} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(1+x)/((1-x)/(1+x))**(1/2),x)
[Out]
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Mathematica [A] time = 0.0197909, size = 19, normalized size = 0.95 \[ \frac{x-1}{\sqrt{\frac{1-x}{x+1}}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(Sqrt[(1 - x)/(1 + x)]*(1 + x)),x]
[Out]
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Maple [A] time = 0.005, size = 17, normalized size = 0.9 \[{(-1+x){\frac{1}{\sqrt{-{\frac{-1+x}{1+x}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(1+x)/((1-x)/(1+x))^(1/2),x)
[Out]
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Maxima [A] time = 0.716299, size = 36, normalized size = 1.8 \[ \frac{2 \, \sqrt{-\frac{x - 1}{x + 1}}}{\frac{x - 1}{x + 1} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x + 1)*sqrt(-(x - 1)/(x + 1))),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.272183, size = 23, normalized size = 1.15 \[ -{\left (x + 1\right )} \sqrt{-\frac{x - 1}{x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x + 1)*sqrt(-(x - 1)/(x + 1))),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{\sqrt{- \frac{x - 1}{x + 1}} \left (x + 1\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(1+x)/((1-x)/(1+x))**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.280352, size = 39, normalized size = 1.95 \[ -\frac{2}{\sqrt{-\frac{x - 1}{x + 1}} + \frac{1}{\sqrt{-\frac{x - 1}{x + 1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x + 1)*sqrt(-(x - 1)/(x + 1))),x, algorithm="giac")
[Out]