Optimal. Leaf size=34 \[ 2 \tanh ^{-1}\left (\frac{2 x}{\sqrt{4 x^2-9}}\right )-\frac{\sqrt{4 x^2-9}}{x} \]
[Out]
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Rubi [A] time = 0.0277707, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ 2 \tanh ^{-1}\left (\frac{2 x}{\sqrt{4 x^2-9}}\right )-\frac{\sqrt{4 x^2-9}}{x} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[-9 + 4*x^2]/x^2,x]
[Out]
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Rubi in Sympy [A] time = 3.50471, size = 27, normalized size = 0.79 \[ 2 \operatorname{atanh}{\left (\frac{2 x}{\sqrt{4 x^{2} - 9}} \right )} - \frac{\sqrt{4 x^{2} - 9}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((4*x**2-9)**(1/2)/x**2,x)
[Out]
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Mathematica [A] time = 0.0135292, size = 35, normalized size = 1.03 \[ 2 \log \left (\sqrt{4 x^2-9}+2 x\right )-\frac{\sqrt{4 x^2-9}}{x} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[-9 + 4*x^2]/x^2,x]
[Out]
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Maple [A] time = 0.004, size = 48, normalized size = 1.4 \[{\frac{1}{9\,x} \left ( 4\,{x}^{2}-9 \right ) ^{{\frac{3}{2}}}}-{\frac{4\,x}{9}\sqrt{4\,{x}^{2}-9}}+\ln \left ( x\sqrt{4}+\sqrt{4\,{x}^{2}-9} \right ) \sqrt{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((4*x^2-9)^(1/2)/x^2,x)
[Out]
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Maxima [A] time = 1.48656, size = 45, normalized size = 1.32 \[ -\frac{\sqrt{4 \, x^{2} - 9}}{x} + 2 \, \log \left (8 \, x + 4 \, \sqrt{4 \, x^{2} - 9}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 - 9)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228035, size = 78, normalized size = 2.29 \[ -\frac{2 \,{\left (2 \, x^{2} - \sqrt{4 \, x^{2} - 9} x\right )} \log \left (-2 \, x + \sqrt{4 \, x^{2} - 9}\right ) + 9}{2 \, x^{2} - \sqrt{4 \, x^{2} - 9} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 - 9)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.681614, size = 19, normalized size = 0.56 \[ 2 \operatorname{acosh}{\left (\frac{2 x}{3} \right )} - \frac{\sqrt{4 x^{2} - 9}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((4*x**2-9)**(1/2)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.207545, size = 59, normalized size = 1.74 \[ -\frac{36}{{\left (2 \, x - \sqrt{4 \, x^{2} - 9}\right )}^{2} + 9} -{\rm ln}\left ({\left (2 \, x - \sqrt{4 \, x^{2} - 9}\right )}^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 - 9)/x^2,x, algorithm="giac")
[Out]