Optimal. Leaf size=25 \[ \frac{2 x \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \]
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Rubi [A] time = 0.042153, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13 \[ \frac{2 x \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b - a/x]/Sqrt[a - b*x],x]
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Rubi in Sympy [A] time = 4.35024, size = 19, normalized size = 0.76 \[ - \frac{2 \sqrt{a - b x}}{\sqrt{- \frac{a}{x} + b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b-a/x)**(1/2)/(-b*x+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0265951, size = 25, normalized size = 1. \[ \frac{2 x \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b - a/x]/Sqrt[a - b*x],x]
[Out]
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Maple [A] time = 0.003, size = 25, normalized size = 1. \[ 2\,{\frac{x}{\sqrt{-bx+a}}\sqrt{-{\frac{-bx+a}{x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b-a/x)^(1/2)/(-b*x+a)^(1/2),x)
[Out]
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Maxima [A] time = 0.783961, size = 7, normalized size = 0.28 \[ -2 i \, \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x)/sqrt(-b*x + a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.260108, size = 41, normalized size = 1.64 \[ \frac{2 \,{\left (b x - a\right )}}{\sqrt{-b x + a} \sqrt{\frac{b x - a}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x)/sqrt(-b*x + a),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- \frac{a}{x} + b}}{\sqrt{a - b x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b-a/x)**(1/2)/(-b*x+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.282074, size = 69, normalized size = 2.76 \[ \frac{2 \,{\left (\sqrt{-{\left (b x - a\right )} b - a b} - \sqrt{-a b}\right )}{\left | b \right |}{\rm sign}\left (x\right )}{b^{2}} + \frac{2 \, \sqrt{-a b}{\left | b \right |}{\rm sign}\left (x\right )}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x)/sqrt(-b*x + a),x, algorithm="giac")
[Out]