Optimal. Leaf size=33 \[ -\frac{1}{2} \sqrt{4 x-x^2} (2-x)-2 \sin ^{-1}\left (1-\frac{x}{2}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0270427, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.364 \[ -\frac{1}{2} \sqrt{4 x-x^2} (2-x)-2 \sin ^{-1}\left (1-\frac{x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[(4 - x)*x],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0.953432, size = 24, normalized size = 0.73 \[ - \frac{\left (- 2 x + 4\right ) \sqrt{- x^{2} + 4 x}}{4} + 2 \operatorname{asin}{\left (\frac{x}{2} - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(((4-x)*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0427216, size = 45, normalized size = 1.36 \[ \frac{1}{2} \sqrt{-(x-4) x} \left (x-\frac{8 \log \left (\sqrt{x-4}+\sqrt{x}\right )}{\sqrt{x-4} \sqrt{x}}-2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[(4 - x)*x],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 28, normalized size = 0.9 \[ -{\frac{-2\,x+4}{4}\sqrt{-{x}^{2}+4\,x}}+2\,\arcsin \left ( x/2-1 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(((4-x)*x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.752189, size = 49, normalized size = 1.48 \[ \frac{1}{2} \, \sqrt{-x^{2} + 4 \, x} x - \sqrt{-x^{2} + 4 \, x} - 2 \, \arcsin \left (-\frac{1}{2} \, x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-(x - 4)*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.265156, size = 47, normalized size = 1.42 \[ \frac{1}{2} \, \sqrt{-x^{2} + 4 \, x}{\left (x - 2\right )} - 4 \, \arctan \left (\frac{\sqrt{-x^{2} + 4 \, x}}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-(x - 4)*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x \left (- x + 4\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(((4-x)*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.260836, size = 34, normalized size = 1.03 \[ \frac{1}{2} \, \sqrt{-x^{2} + 4 \, x}{\left (x - 2\right )} + 2 \, \arcsin \left (\frac{1}{2} \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-(x - 4)*x),x, algorithm="giac")
[Out]