Optimal. Leaf size=17 \[ \text{Int}\left (\sqrt{x-x^2} F(x),x\right ) \]
[Out]
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Rubi [A] time = 0.173845, 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. \[ \text{Int}\left (\sqrt{1-x} \sqrt{x} F(x),x\right ) \]
Verification is Not applicable to the result.
[In] Int[Sqrt[1 - x]*Sqrt[x]*F[x],x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ 2 \int ^{\sqrt{x}} x^{2} \sqrt{- x^{2} + 1} F{\left (x^{2} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F(x)*(1-x)**(1/2)*x**(1/2),x)
[Out]
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Mathematica [A] time = 0.0320601, size = 0, normalized size = 0. \[ \int \sqrt{1-x} \sqrt{x} F(x) \, dx \]
Verification is Not applicable to the result.
[In] Integrate[Sqrt[1 - x]*Sqrt[x]*F[x],x]
[Out]
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Maple [A] time = 0.025, size = 0, normalized size = 0. \[ \int F \left ( x \right ) \sqrt{1-x}\sqrt{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F(x)*(1-x)^(1/2)*x^(1/2),x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x} \sqrt{-x + 1} F\left (x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)*sqrt(-x + 1)*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)*sqrt(-x + 1)*F(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x} \sqrt{- x + 1} F{\left (x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F(x)*(1-x)**(1/2)*x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{x} \sqrt{-x + 1} F\left (x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x)*sqrt(-x + 1)*F(x),x, algorithm="giac")
[Out]