Optimal. Leaf size=34 \[ 3 \tanh ^{-1}\left (\frac{3 x}{\sqrt{9 x^2-1}}\right )-\frac{\sqrt{9 x^2-1}}{x} \]
[Out]
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Rubi [A] time = 0.0222532, 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 \[ 3 \tanh ^{-1}\left (\frac{3 x}{\sqrt{9 x^2-1}}\right )-\frac{\sqrt{9 x^2-1}}{x} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[-1 + 9*x^2]/x^2,x]
[Out]
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Rubi in Sympy [A] time = 1.68437, size = 27, normalized size = 0.79 \[ 3 \operatorname{atanh}{\left (\frac{3 x}{\sqrt{9 x^{2} - 1}} \right )} - \frac{\sqrt{9 x^{2} - 1}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((9*x**2-1)**(1/2)/x**2,x)
[Out]
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Mathematica [A] time = 0.0155297, size = 35, normalized size = 1.03 \[ 3 \log \left (\sqrt{9 x^2-1}+3 x\right )-\frac{\sqrt{9 x^2-1}}{x} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[-1 + 9*x^2]/x^2,x]
[Out]
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Maple [A] time = 0.01, size = 47, normalized size = 1.4 \[{\frac{1}{x} \left ( 9\,{x}^{2}-1 \right ) ^{{\frac{3}{2}}}}-9\,x\sqrt{9\,{x}^{2}-1}+\ln \left ( x\sqrt{9}+\sqrt{9\,{x}^{2}-1} \right ) \sqrt{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((9*x^2-1)^(1/2)/x^2,x)
[Out]
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Maxima [A] time = 1.48653, size = 45, normalized size = 1.32 \[ -\frac{\sqrt{9 \, x^{2} - 1}}{x} + 3 \, \log \left (18 \, x + 6 \, \sqrt{9 \, x^{2} - 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(9*x^2 - 1)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211885, size = 78, normalized size = 2.29 \[ -\frac{3 \,{\left (3 \, x^{2} - \sqrt{9 \, x^{2} - 1} x\right )} \log \left (-3 \, x + \sqrt{9 \, x^{2} - 1}\right ) + 1}{3 \, x^{2} - \sqrt{9 \, x^{2} - 1} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(9*x^2 - 1)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.343018, size = 17, normalized size = 0.5 \[ 3 \operatorname{acosh}{\left (3 x \right )} - \frac{\sqrt{9 x^{2} - 1}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((9*x**2-1)**(1/2)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.21771, size = 59, normalized size = 1.74 \[ -\frac{6}{{\left (3 \, x - \sqrt{9 \, x^{2} - 1}\right )}^{2} + 1} - \frac{3}{2} \,{\rm ln}\left ({\left (3 \, x - \sqrt{9 \, x^{2} - 1}\right )}^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(9*x^2 - 1)/x^2,x, algorithm="giac")
[Out]