Optimal. Leaf size=11 \[ \frac{2}{\sqrt{\frac{1}{x}+1}} \]
[Out]
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Rubi [A] time = 0.0135279, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{2}{\sqrt{\frac{1}{x}+1}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 + x^(-1)]/(1 + x)^2,x]
[Out]
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Rubi in Sympy [A] time = 1.34967, size = 8, normalized size = 0.73 \[ \frac{2}{\sqrt{1 + \frac{1}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+1/x)**(1/2)/(1+x)**2,x)
[Out]
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Mathematica [A] time = 0.0147826, size = 17, normalized size = 1.55 \[ \frac{2 \sqrt{\frac{1}{x}+1} x}{x+1} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 + x^(-1)]/(1 + x)^2,x]
[Out]
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Maple [A] time = 0.005, size = 18, normalized size = 1.6 \[ 2\,{\frac{x}{1+x}\sqrt{{\frac{1+x}{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+1/x)^(1/2)/(1+x)^2,x)
[Out]
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Maxima [A] time = 0.88832, size = 15, normalized size = 1.36 \[ \frac{2}{\sqrt{\frac{x + 1}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(1/x + 1)/(x + 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.28111, size = 15, normalized size = 1.36 \[ \frac{2}{\sqrt{\frac{x + 1}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(1/x + 1)/(x + 1)^2,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{1 + \frac{1}{x}}}{\left (x + 1\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+1/x)**(1/2)/(1+x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.269729, size = 31, normalized size = 2.82 \[ \frac{2 \,{\rm sign}\left (x\right )}{x - \sqrt{x^{2} + x} + 1} - 2 \,{\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(1/x + 1)/(x + 1)^2,x, algorithm="giac")
[Out]