Optimal. Leaf size=37 \[ \sqrt{3-x^2}-\sqrt{3} \tanh ^{-1}\left (\frac{\sqrt{3-x^2}}{\sqrt{3}}\right ) \]
[Out]
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Rubi [A] time = 0.0473773, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ \sqrt{3-x^2}-\sqrt{3} \tanh ^{-1}\left (\frac{\sqrt{3-x^2}}{\sqrt{3}}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[3 - x^2]/x,x]
[Out]
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Rubi in Sympy [A] time = 2.37152, size = 29, normalized size = 0.78 \[ \sqrt{- x^{2} + 3} - \sqrt{3} \operatorname{atanh}{\left (\frac{\sqrt{3} \sqrt{- x^{2} + 3}}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**2+3)**(1/2)/x,x)
[Out]
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Mathematica [A] time = 0.0214785, size = 41, normalized size = 1.11 \[ \sqrt{3-x^2}-\sqrt{3} \log \left (\sqrt{9-3 x^2}+3\right )+\sqrt{3} \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[3 - x^2]/x,x]
[Out]
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Maple [A] time = 0.006, size = 30, normalized size = 0.8 \[ \sqrt{-{x}^{2}+3}-\sqrt{3}{\it Artanh} \left ({\sqrt{3}{\frac{1}{\sqrt{-{x}^{2}+3}}}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^2+3)^(1/2)/x,x)
[Out]
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Maxima [A] time = 1.51444, size = 55, normalized size = 1.49 \[ -\sqrt{3} \log \left (\frac{2 \, \sqrt{3} \sqrt{-x^{2} + 3}}{{\left | x \right |}} + \frac{6}{{\left | x \right |}}\right ) + \sqrt{-x^{2} + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 3)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216663, size = 54, normalized size = 1.46 \[ \frac{1}{2} \, \sqrt{3} \log \left (-\frac{x^{2} + 2 \, \sqrt{3} \sqrt{-x^{2} + 3} - 6}{x^{2}}\right ) + \sqrt{-x^{2} + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 3)/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.22713, size = 88, normalized size = 2.38 \[ \begin{cases} i \sqrt{x^{2} - 3} - \sqrt{3} \log{\left (x \right )} + \frac{\sqrt{3} \log{\left (x^{2} \right )}}{2} + \sqrt{3} i \operatorname{asin}{\left (\frac{\sqrt{3}}{x} \right )} & \text{for}\: \frac{\left |{x^{2}}\right |}{3} > 1 \\\sqrt{- x^{2} + 3} + \frac{\sqrt{3} \log{\left (x^{2} \right )}}{2} - \sqrt{3} \log{\left (\sqrt{- \frac{x^{2}}{3} + 1} + 1 \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**2+3)**(1/2)/x,x)
[Out]
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GIAC/XCAS [A] time = 0.226267, size = 63, normalized size = 1.7 \[ \frac{1}{2} \, \sqrt{3}{\rm ln}\left (\frac{\sqrt{3} - \sqrt{-x^{2} + 3}}{\sqrt{3} + \sqrt{-x^{2} + 3}}\right ) + \sqrt{-x^{2} + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 3)/x,x, algorithm="giac")
[Out]