Optimal. Leaf size=31 \[ -\frac{\sqrt{b-\frac{a}{x^2}}}{2 x \sqrt{a-b x^2}} \]
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Rubi [A] time = 0.114928, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.107 \[ -\frac{\sqrt{b-\frac{a}{x^2}}}{2 x \sqrt{a-b x^2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b - a/x^2]/(x^2*Sqrt[a - b*x^2]),x]
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Rubi in Sympy [A] time = 5.78084, size = 24, normalized size = 0.77 \[ \frac{\sqrt{a - b x^{2}}}{2 x^{3} \sqrt{- \frac{a}{x^{2}} + b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b-a/x**2)**(1/2)/x**2/(-b*x**2+a)**(1/2),x)
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Mathematica [A] time = 0.0250569, size = 38, normalized size = 1.23 \[ \frac{\sqrt{b-\frac{a}{x^2}} \sqrt{a-b x^2}}{2 b x^3-2 a x} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b - a/x^2]/(x^2*Sqrt[a - b*x^2]),x]
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Maple [A] time = 0.003, size = 31, normalized size = 1. \[ -{\frac{1}{2\,x}\sqrt{-{\frac{-b{x}^{2}+a}{{x}^{2}}}}{\frac{1}{\sqrt{-b{x}^{2}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b-a/x^2)^(1/2)/x^2/(-b*x^2+a)^(1/2),x)
[Out]
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Maxima [A] time = 0.774443, size = 7, normalized size = 0.23 \[ \frac{i}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)/(sqrt(-b*x^2 + a)*x^2),x, algorithm="maxima")
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Fricas [A] time = 0.270704, size = 59, normalized size = 1.9 \[ -\frac{\sqrt{-b x^{2} + a}{\left (x^{2} - 1\right )} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{2 \,{\left (b x^{3} - a x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)/(sqrt(-b*x^2 + a)*x^2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- \frac{a}{x^{2}} + b}}{x^{2} \sqrt{a - b x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b-a/x**2)**(1/2)/x**2/(-b*x**2+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.275152, size = 27, normalized size = 0.87 \[ -\frac{{\rm sign}\left (b x^{2} - a\right ){\rm sign}\left (x\right )}{2 \, i x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)/(sqrt(-b*x^2 + a)*x^2),x, algorithm="giac")
[Out]