Optimal. Leaf size=20 \[ \frac{F\left (\sin ^{-1}\left (\sqrt{\frac{5}{2}} x\right )|-\frac{2}{5}\right )}{\sqrt{5}} \]
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Rubi [A] time = 0.0304281, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{F\left (\sin ^{-1}\left (\sqrt{\frac{5}{2}} x\right )|-\frac{2}{5}\right )}{\sqrt{5}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[2 - 5*x^2]*Sqrt[1 + x^2]),x]
[Out]
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Rubi in Sympy [A] time = 4.95618, size = 20, normalized size = 1. \[ \frac{\sqrt{5} F\left (\operatorname{asin}{\left (\frac{\sqrt{10} x}{2} \right )}\middle | - \frac{2}{5}\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-5*x**2+2)**(1/2)/(x**2+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0343294, size = 20, normalized size = 1. \[ \frac{F\left (\sin ^{-1}\left (\sqrt{\frac{5}{2}} x\right )|-\frac{2}{5}\right )}{\sqrt{5}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[2 - 5*x^2]*Sqrt[1 + x^2]),x]
[Out]
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Maple [A] time = 0.052, size = 25, normalized size = 1.3 \[{\frac{\sqrt{5}}{5}{\it EllipticF} \left ({\frac{\sqrt{5}\sqrt{2}x}{2}},{\frac{i}{5}}\sqrt{5}\sqrt{2} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-5*x^2+2)^(1/2)/(x^2+1)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x^{2} + 1} \sqrt{-5 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 + 1)*sqrt(-5*x^2 + 2)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{x^{2} + 1} \sqrt{-5 \, x^{2} + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 + 1)*sqrt(-5*x^2 + 2)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- 5 x^{2} + 2} \sqrt{x^{2} + 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-5*x**2+2)**(1/2)/(x**2+1)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x^{2} + 1} \sqrt{-5 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 + 1)*sqrt(-5*x^2 + 2)),x, algorithm="giac")
[Out]