Optimal. Leaf size=28 \[ \frac{x \log (x) \sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \]
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Rubi [A] time = 0.0530788, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.12 \[ \frac{x \log (x) \sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b - a/x^2]/Sqrt[a - b*x^2],x]
[Out]
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Rubi in Sympy [A] time = 5.15388, size = 26, normalized size = 0.93 \[ - \frac{\sqrt{a - b x^{2}} \log{\left (x \right )}}{x \sqrt{- \frac{a}{x^{2}} + b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b-a/x**2)**(1/2)/(-b*x**2+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.11024, size = 0, normalized size = 0. \[ \int \frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[Sqrt[b - a/x^2]/Sqrt[a - b*x^2],x]
[Out]
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Maple [A] time = 0.011, size = 42, normalized size = 1.5 \[ -{\frac{x\ln \left ( x \right ) }{b{x}^{2}-a}\sqrt{{\frac{b{x}^{2}-a}{{x}^{2}}}}\sqrt{-b{x}^{2}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x)
[Out]
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Maxima [A] time = 0.719973, size = 5, normalized size = 0.18 \[ -i \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)/sqrt(-b*x^2 + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.291698, size = 69, normalized size = 2.46 \[ -\arctan \left (\frac{\sqrt{-b x^{2} + a}{\left (x^{3} + x\right )} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{b x^{4} -{\left (a + b\right )} x^{2} + a}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)/sqrt(-b*x^2 + a),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- \frac{a}{x^{2}} + b}}{\sqrt{a - b x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b-a/x**2)**(1/2)/(-b*x**2+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.275199, size = 42, normalized size = 1.5 \[ -\frac{1}{2} \, i{\rm ln}\left ({\left (b x^{2} - a\right )} i + a i\right ){\rm sign}\left (b x^{2} - a\right ){\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)/sqrt(-b*x^2 + a),x, algorithm="giac")
[Out]