Optimal. Leaf size=27 \[ 10 \tanh ^{-1}\left (\frac{x}{\sqrt{x^2-4}}\right )+\tanh ^{-1}\left (\frac{x}{\sqrt{x^2-1}}\right ) \]
[Out]
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Rubi [A] time = 0.0163863, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ 10 \tanh ^{-1}\left (\frac{x}{\sqrt{x^2-4}}\right )+\tanh ^{-1}\left (\frac{x}{\sqrt{x^2-1}}\right ) \]
Antiderivative was successfully verified.
[In] Int[10/Sqrt[-4 + x^2] + 1/Sqrt[-1 + x^2],x]
[Out]
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Rubi in Sympy [A] time = 0.905945, size = 24, normalized size = 0.89 \[ 10 \operatorname{atanh}{\left (\frac{x}{\sqrt{x^{2} - 4}} \right )} + \operatorname{atanh}{\left (\frac{x}{\sqrt{x^{2} - 1}} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(10/(x**2-4)**(1/2)+1/(x**2-1)**(1/2),x)
[Out]
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Mathematica [B] time = 0.0119472, size = 71, normalized size = 2.63 \[ -5 \log \left (1-\frac{x}{\sqrt{x^2-4}}\right )+5 \log \left (\frac{x}{\sqrt{x^2-4}}+1\right )-\frac{1}{2} \log \left (1-\frac{x}{\sqrt{x^2-1}}\right )+\frac{1}{2} \log \left (\frac{x}{\sqrt{x^2-1}}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[10/Sqrt[-4 + x^2] + 1/Sqrt[-1 + x^2],x]
[Out]
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Maple [A] time = 0.002, size = 24, normalized size = 0.9 \[ \ln \left ( x+\sqrt{{x}^{2}-1} \right ) +10\,\ln \left ( x+\sqrt{{x}^{2}-4} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(10/(x^2-4)^(1/2)+1/(x^2-1)^(1/2),x)
[Out]
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Maxima [A] time = 1.36558, size = 42, normalized size = 1.56 \[ \log \left (2 \, x + 2 \, \sqrt{x^{2} - 1}\right ) + 10 \, \log \left (2 \, x + 2 \, \sqrt{x^{2} - 4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(x^2 - 1) + 10/sqrt(x^2 - 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210409, size = 39, normalized size = 1.44 \[ -\log \left (-x + \sqrt{x^{2} - 1}\right ) - 10 \, \log \left (-x + \sqrt{x^{2} - 4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(x^2 - 1) + 10/sqrt(x^2 - 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.194793, size = 8, normalized size = 0.3 \[ 10 \operatorname{acosh}{\left (\frac{x}{2} \right )} + \operatorname{acosh}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(10/(x**2-4)**(1/2)+1/(x**2-1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.206359, size = 42, normalized size = 1.56 \[ -{\rm ln}\left ({\left | -x + \sqrt{x^{2} - 1} \right |}\right ) - 10 \,{\rm ln}\left ({\left | -x + \sqrt{x^{2} - 4} \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(x^2 - 1) + 10/sqrt(x^2 - 4),x, algorithm="giac")
[Out]