Optimal. Leaf size=20 \[ -\frac{\sqrt{6 x-x^2}}{3 x} \]
[Out]
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Rubi [A] time = 0.0191091, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ -\frac{\sqrt{6 x-x^2}}{3 x} \]
Antiderivative was successfully verified.
[In] Int[1/(x*Sqrt[6*x - x^2]),x]
[Out]
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Rubi in Sympy [A] time = 1.7664, size = 14, normalized size = 0.7 \[ - \frac{\sqrt{- x^{2} + 6 x}}{3 x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(-x**2+6*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0135887, size = 17, normalized size = 0.85 \[ \frac{x-6}{3 \sqrt{-(x-6) x}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*Sqrt[6*x - x^2]),x]
[Out]
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Maple [A] time = 0.004, size = 17, normalized size = 0.9 \[{\frac{-6+x}{3}{\frac{1}{\sqrt{-{x}^{2}+6\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(-x^2+6*x)^(1/2),x)
[Out]
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Maxima [A] time = 0.783018, size = 22, normalized size = 1.1 \[ -\frac{\sqrt{-x^{2} + 6 \, x}}{3 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^2 + 6*x)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.261602, size = 22, normalized size = 1.1 \[ -\frac{\sqrt{-x^{2} + 6 \, x}}{3 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^2 + 6*x)*x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{x \sqrt{- x \left (x - 6\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(-x**2+6*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.26747, size = 34, normalized size = 1.7 \[ \frac{2}{3 \,{\left (\frac{\sqrt{-x^{2} + 6 \, x} - 3}{x - 3} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^2 + 6*x)*x),x, algorithm="giac")
[Out]