Optimal. Leaf size=6 \[ \sinh ^{-1}\left (\frac{x}{2}\right ) \]
[Out]
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Rubi [A] time = 0.00359629, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \sinh ^{-1}\left (\frac{x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[4 + x^2],x]
[Out]
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Rubi in Sympy [A] time = 0.5122, size = 3, normalized size = 0.5 \[ \operatorname{asinh}{\left (\frac{x}{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**2+4)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00512773, size = 6, normalized size = 1. \[ \sinh ^{-1}\left (\frac{x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[4 + x^2],x]
[Out]
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Maple [A] time = 0.002, size = 5, normalized size = 0.8 \[{\it Arcsinh} \left ({\frac{x}{2}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^2+4)^(1/2),x)
[Out]
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Maxima [A] time = 1.49965, size = 5, normalized size = 0.83 \[ \operatorname{arsinh}\left (\frac{1}{2} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(x^2 + 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201026, size = 19, normalized size = 3.17 \[ -\log \left (-x + \sqrt{x^{2} + 4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(x^2 + 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.14089, size = 3, normalized size = 0.5 \[ \operatorname{asinh}{\left (\frac{x}{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**2+4)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.203885, size = 19, normalized size = 3.17 \[ -{\rm ln}\left (-x + \sqrt{x^{2} + 4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(x^2 + 4),x, algorithm="giac")
[Out]