Optimal. Leaf size=14 \[ -2 \log \left (\sqrt{4-x}+1\right ) \]
[Out]
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Rubi [A] time = 0.0342119, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -2 \log \left (\sqrt{4-x}+1\right ) \]
Antiderivative was successfully verified.
[In] Int[(4 + Sqrt[4 - x] - x)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.25729, size = 12, normalized size = 0.86 \[ - 2 \log{\left (\sqrt{- x + 4} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(4-x+(4-x)**(1/2)),x)
[Out]
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Mathematica [A] time = 0.00647614, size = 14, normalized size = 1. \[ -2 \log \left (\sqrt{4-x}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(4 + Sqrt[4 - x] - x)^(-1),x]
[Out]
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Maple [A] time = 0.017, size = 18, normalized size = 1.3 \[ -\ln \left ( -3+x \right ) -2\,{\it Artanh} \left ( \sqrt{4-x} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(4-x+(4-x)^(1/2)),x)
[Out]
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Maxima [A] time = 0.719177, size = 16, normalized size = 1.14 \[ -2 \, \log \left (\sqrt{-x + 4} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(x - sqrt(-x + 4) - 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.262294, size = 16, normalized size = 1.14 \[ -2 \, \log \left (\sqrt{-x + 4} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(x - sqrt(-x + 4) - 4),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \int \frac{1}{x - \sqrt{- x + 4} - 4}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4-x+(4-x)**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.285926, size = 16, normalized size = 1.14 \[ -2 \,{\rm ln}\left (\sqrt{-x + 4} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(x - sqrt(-x + 4) - 4),x, algorithm="giac")
[Out]