Optimal. Leaf size=24 \[ -\frac{2 \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \]
[Out]
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Rubi [A] time = 0.129611, antiderivative size = 24, 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 \[ -\frac{2 \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b - a/x]/(x*Sqrt[a - b*x]),x]
[Out]
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Rubi in Sympy [A] time = 5.55558, size = 19, normalized size = 0.79 \[ \frac{2 \sqrt{a - b x}}{x \sqrt{- \frac{a}{x} + b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b-a/x)**(1/2)/x/(-b*x+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0265813, size = 24, normalized size = 1. \[ -\frac{2 \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b - a/x]/(x*Sqrt[a - b*x]),x]
[Out]
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Maple [A] time = 0.003, size = 24, normalized size = 1. \[ -2\,{\frac{1}{\sqrt{-bx+a}}\sqrt{-{\frac{-bx+a}{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b-a/x)^(1/2)/x/(-b*x+a)^(1/2),x)
[Out]
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Maxima [A] time = 0.757043, size = 7, normalized size = 0.29 \[ \frac{2 i}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x)/(sqrt(-b*x + a)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.262101, size = 43, normalized size = 1.79 \[ \frac{2 \, \sqrt{-b x + a} \sqrt{\frac{b x - a}{x}}}{b x - a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x)/(sqrt(-b*x + a)*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- \frac{a}{x} + b}}{x \sqrt{a - b x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b-a/x)**(1/2)/x/(-b*x+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.287364, size = 57, normalized size = 2.38 \[ \frac{2 \,{\left (\frac{b^{3}}{\sqrt{-{\left (b x - a\right )} b - a b}} - \frac{b^{3}}{\sqrt{-a b}}\right )}{\left | b \right |}{\rm sign}\left (x\right )}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x)/(sqrt(-b*x + a)*x),x, algorithm="giac")
[Out]