Optimal. Leaf size=37 \[ -\frac{1}{2} \sqrt{x^2-8 x} (4-x)-16 \tanh ^{-1}\left (\frac{x}{\sqrt{x^2-8 x}}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0197001, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ -\frac{1}{2} \sqrt{x^2-8 x} (4-x)-16 \tanh ^{-1}\left (\frac{x}{\sqrt{x^2-8 x}}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[-8*x + x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.48839, size = 32, normalized size = 0.86 \[ - \frac{\left (- 2 x + 8\right ) \sqrt{x^{2} - 8 x}}{4} - 16 \operatorname{atanh}{\left (\frac{x}{\sqrt{x^{2} - 8 x}} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2-8*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0440485, size = 44, normalized size = 1.19 \[ \frac{1}{2} \sqrt{(x-8) x} \left (x-\frac{32 \log \left (\sqrt{x-8}+\sqrt{x}\right )}{\sqrt{x-8} \sqrt{x}}-4\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[-8*x + x^2],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 33, normalized size = 0.9 \[{\frac{2\,x-8}{4}\sqrt{{x}^{2}-8\,x}}-8\,\ln \left ( x-4+\sqrt{{x}^{2}-8\,x} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2-8*x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.726829, size = 58, normalized size = 1.57 \[ \frac{1}{2} \, \sqrt{x^{2} - 8 \, x} x - 2 \, \sqrt{x^{2} - 8 \, x} - 8 \, \log \left (2 \, x + 2 \, \sqrt{x^{2} - 8 \, x} - 8\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^2 - 8*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.214963, size = 144, normalized size = 3.89 \[ -\frac{x^{4} - 16 \, x^{3} + 76 \, x^{2} - 16 \,{\left (x^{2} - \sqrt{x^{2} - 8 \, x}{\left (x - 4\right )} - 8 \, x + 8\right )} \log \left (-x + \sqrt{x^{2} - 8 \, x} + 4\right ) -{\left (x^{3} - 12 \, x^{2} + 36 \, x - 16\right )} \sqrt{x^{2} - 8 \, x} - 96 \, x - 32}{2 \,{\left (x^{2} - \sqrt{x^{2} - 8 \, x}{\left (x - 4\right )} - 8 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^2 - 8*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x^{2} - 8 x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2-8*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210566, size = 45, normalized size = 1.22 \[ \frac{1}{2} \, \sqrt{x^{2} - 8 \, x}{\left (x - 4\right )} + 8 \,{\rm ln}\left ({\left | -x + \sqrt{x^{2} - 8 \, x} + 4 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^2 - 8*x),x, algorithm="giac")
[Out]