Optimal. Leaf size=17 \[ \text{Int}\left (\sqrt{x-x^2} F(x),x\right ) \]
[Out]
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Rubi [A] time = 0.0571509, 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. \[ \text{Int}\left (\sqrt{x-x^2} F(x),x\right ) \]
Verification is Not applicable to the result.
[In] Int[Sqrt[x - x^2]*F[x],x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \frac{2 \sqrt{- x^{2} + x} \int ^{\sqrt{x}} x^{2} \sqrt{- x^{2} + 1} F{\left (x^{2} \right )}\, dx}{\sqrt{x} \sqrt{- x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F(x)*(-x**2+x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.100756, size = 0, normalized size = 0. \[ \int \sqrt{x-x^2} F(x) \, dx \]
Verification is Not applicable to the result.
[In] Integrate[Sqrt[x - x^2]*F[x],x]
[Out]
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Maple [A] time = 0.026, size = 0, normalized size = 0. \[ \int F \left ( x \right ) \sqrt{-{x}^{2}+x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F(x)*(-x^2+x)^(1/2),x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{-x^{2} + x} F\left (x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + x)*F(x),x, algorithm="maxima")
[Out]
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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(sqrt(-x^2 + x)*F(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{- x \left (x - 1\right )} F{\left (x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F(x)*(-x**2+x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{-x^{2} + x} F\left (x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + x)*F(x),x, algorithm="giac")
[Out]