Optimal. Leaf size=18 \[ \frac{\sqrt{x-1} \sqrt{x+1}}{x} \]
[Out]
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Rubi [A] time = 0.0247513, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{\sqrt{x-1} \sqrt{x+1}}{x} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]
[Out]
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Rubi in Sympy [A] time = 2.60379, size = 14, normalized size = 0.78 \[ \frac{\sqrt{x - 1} \sqrt{x + 1}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(-1+x)**(1/2)/(1+x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0137036, size = 18, normalized size = 1. \[ \frac{\sqrt{x-1} \sqrt{x+1}}{x} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[-1 + x]*x^2*Sqrt[1 + x]),x]
[Out]
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Maple [A] time = 0.004, size = 15, normalized size = 0.8 \[{\frac{1}{x}\sqrt{-1+x}\sqrt{1+x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(-1+x)^(1/2)/(1+x)^(1/2),x)
[Out]
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Maxima [A] time = 1.48839, size = 15, normalized size = 0.83 \[ \frac{\sqrt{x^{2} - 1}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 1)*sqrt(x - 1)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226151, size = 30, normalized size = 1.67 \[ -\frac{1}{\sqrt{x + 1} \sqrt{x - 1} x - x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 1)*sqrt(x - 1)*x^2),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(-1+x)**(1/2)/(1+x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.21815, size = 28, normalized size = 1.56 \[ \frac{8}{{\left (\sqrt{x + 1} - \sqrt{x - 1}\right )}^{4} + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 1)*sqrt(x - 1)*x^2),x, algorithm="giac")
[Out]