Optimal. Leaf size=26 \[ -\frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \]
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Rubi [A] time = 0.112253, antiderivative size = 26, 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 \[ -\frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b - a/x^2]/(x*Sqrt[a - b*x^2]),x]
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Rubi in Sympy [A] time = 5.9837, size = 22, normalized size = 0.85 \[ \frac{\sqrt{a - b x^{2}}}{x^{2} \sqrt{- \frac{a}{x^{2}} + b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b-a/x**2)**(1/2)/x/(-b*x**2+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0334872, size = 26, normalized size = 1. \[ -\frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b - a/x^2]/(x*Sqrt[a - b*x^2]),x]
[Out]
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Maple [A] time = 0.004, size = 28, normalized size = 1.1 \[ -{1\sqrt{-{\frac{-b{x}^{2}+a}{{x}^{2}}}}{\frac{1}{\sqrt{-b{x}^{2}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b-a/x^2)^(1/2)/x/(-b*x^2+a)^(1/2),x)
[Out]
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Maxima [A] time = 0.731808, size = 9, normalized size = 0.35 \[ \frac{i}{\sqrt{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)/(sqrt(-b*x^2 + a)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.266722, size = 55, normalized size = 2.12 \[ -\frac{\sqrt{-b x^{2} + a}{\left (x - 1\right )} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{b x^{2} - a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)/(sqrt(-b*x^2 + a)*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- \frac{a}{x^{2}} + b}}{x \sqrt{a - b x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b-a/x**2)**(1/2)/x/(-b*x**2+a)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{b - \frac{a}{x^{2}}}}{\sqrt{-b x^{2} + a} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)/(sqrt(-b*x^2 + a)*x),x, algorithm="giac")
[Out]