Optimal. Leaf size=32 \[ \frac{\sqrt{1-x^2} F\left (\sin ^{-1}(x)|-\frac{5}{2}\right )}{\sqrt{2} \sqrt{x^2-1}} \]
[Out]
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Rubi [A] time = 0.0458628, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095 \[ \frac{\sqrt{1-x^2} F\left (\sin ^{-1}(x)|-\frac{5}{2}\right )}{\sqrt{2} \sqrt{x^2-1}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[-1 + x^2]*Sqrt[2 + 5*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 8.69443, size = 31, normalized size = 0.97 \[ \frac{\sqrt{2} \sqrt{- x^{2} + 1} F\left (\operatorname{asin}{\left (x \right )}\middle | - \frac{5}{2}\right )}{2 \sqrt{x^{2} - 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**2-1)**(1/2)/(5*x**2+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0326258, size = 32, normalized size = 1. \[ \frac{\sqrt{1-x^2} F\left (\sin ^{-1}(x)|-\frac{5}{2}\right )}{\sqrt{2} \sqrt{x^2-1}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[-1 + x^2]*Sqrt[2 + 5*x^2]),x]
[Out]
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Maple [A] time = 0.046, size = 43, normalized size = 1.3 \[{-{\frac{i}{5}}{\it EllipticF} \left ({\frac{i}{2}}\sqrt{5}\sqrt{2}x,{\frac{i}{5}}\sqrt{5}\sqrt{2} \right ) \sqrt{5}\sqrt{-{x}^{2}+1}{\frac{1}{\sqrt{{x}^{2}-1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^2-1)^(1/2)/(5*x^2+2)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{5 \, x^{2} + 2} \sqrt{x^{2} - 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x^2 + 2)*sqrt(x^2 - 1)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{5 \, x^{2} + 2} \sqrt{x^{2} - 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x^2 + 2)*sqrt(x^2 - 1)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{\left (x - 1\right ) \left (x + 1\right )} \sqrt{5 x^{2} + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**2-1)**(1/2)/(5*x**2+2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{5 \, x^{2} + 2} \sqrt{x^{2} - 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x^2 + 2)*sqrt(x^2 - 1)),x, algorithm="giac")
[Out]