Optimal. Leaf size=17 \[ \text{Int}\left (\frac{F(x)}{\sqrt{x-x^2}},x\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0601219, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{F(x)}{\sqrt{x-x^2}},x\right ) \]
Verification is Not applicable to the result.
[In] Int[F[x]/Sqrt[x - x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \frac{2 \sqrt{- x^{2} + x} \int ^{\sqrt{x}} \frac{F{\left (x^{2} \right )}}{\sqrt{- x^{2} + 1}}\, dx}{\sqrt{x} \sqrt{- x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F(x)/(-x**2+x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.109296, size = 0, normalized size = 0. \[ \int \frac{F(x)}{\sqrt{x-x^2}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[F[x]/Sqrt[x - x^2],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.028, size = 0, normalized size = 0. \[ \int{F \left ( x \right ){\frac{1}{\sqrt{-{x}^{2}+x}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F(x)/(-x^2+x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{F\left (x\right )}{\sqrt{-x^{2} + x}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F(x)/sqrt(-x^2 + x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F(x)/sqrt(-x^2 + x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{F{\left (x \right )}}{\sqrt{- x \left (x - 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F(x)/(-x**2+x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{F\left (x\right )}{\sqrt{-x^{2} + x}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F(x)/sqrt(-x^2 + x),x, algorithm="giac")
[Out]