Optimal. Leaf size=29 \[ -\frac{2 \sqrt{b-\frac{a}{x}}}{3 x \sqrt{a-b x}} \]
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Rubi [A] time = 0.123482, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.115 \[ -\frac{2 \sqrt{b-\frac{a}{x}}}{3 x \sqrt{a-b x}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b - a/x]/(x^2*Sqrt[a - b*x]),x]
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Rubi in Sympy [A] time = 5.40434, size = 22, normalized size = 0.76 \[ \frac{2 \sqrt{a - b x}}{3 x^{2} \sqrt{- \frac{a}{x} + b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b-a/x)**(1/2)/x**2/(-b*x+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0339624, size = 29, normalized size = 1. \[ -\frac{2 \sqrt{b-\frac{a}{x}}}{3 x \sqrt{a-b x}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b - a/x]/(x^2*Sqrt[a - b*x]),x]
[Out]
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Maple [A] time = 0.003, size = 27, normalized size = 0.9 \[ -{\frac{2}{3\,x}\sqrt{-{\frac{-bx+a}{x}}}{\frac{1}{\sqrt{-bx+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b-a/x)^(1/2)/x^2/(-b*x+a)^(1/2),x)
[Out]
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Maxima [A] time = 0.802035, size = 7, normalized size = 0.24 \[ \frac{2 i}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x)/(sqrt(-b*x + a)*x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265394, size = 47, normalized size = 1.62 \[ \frac{2 \, \sqrt{-b x + a} \sqrt{\frac{b x - a}{x}}}{3 \,{\left (b x^{2} - a x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x)/(sqrt(-b*x + a)*x^2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- \frac{a}{x} + b}}{x^{2} \sqrt{a - b x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b-a/x)**(1/2)/x**2/(-b*x+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.282479, size = 81, normalized size = 2.79 \[ \frac{2 \,{\left (\frac{b^{5}}{{\left ({\left (b x - a\right )} b + a b\right )} \sqrt{-{\left (b x - a\right )} b - a b}} - \frac{b^{4}}{\sqrt{-a b} a}\right )}{\left | b \right |}{\rm sign}\left (x\right )}{3 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x)/(sqrt(-b*x + a)*x^2),x, algorithm="giac")
[Out]