3.903 \(\int \sqrt {1-x} \sqrt {x} F(x) \, dx\)

Optimal. Leaf size=17 \[ \text {Int}\left (\sqrt {x-x^2} F(x),x\right ) \]

[Out]

CannotIntegrate(F(x)*(-x^2+x)^(1/2),x)

________________________________________________________________________________________

Rubi [A]  time = 0.10, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \sqrt {1-x} \sqrt {x} F(x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sqrt[1 - x]*Sqrt[x]*F[x],x]

[Out]

Defer[Int][Sqrt[x - x^2]*F[x], x]

Rubi steps

\begin {align*} \int \sqrt {1-x} \sqrt {x} F(x) \, dx &=\int \sqrt {x-x^2} F(x) \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \sqrt {1-x} \sqrt {x} F(x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sqrt[1 - x]*Sqrt[x]*F[x],x]

[Out]

Integrate[Sqrt[1 - x]*Sqrt[x]*F[x], x]

________________________________________________________________________________________

fricas [A]  time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\sqrt {x} \sqrt {-x + 1} F\relax (x), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x)*(1-x)^(1/2)*x^(1/2),x, algorithm="fricas")

[Out]

integral(sqrt(x)*sqrt(-x + 1)*F(x), x)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {x} \sqrt {-x + 1} F\relax (x)\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x)*(1-x)^(1/2)*x^(1/2),x, algorithm="giac")

[Out]

integrate(sqrt(x)*sqrt(-x + 1)*F(x), x)

________________________________________________________________________________________

maple [A]  time = 0.07, size = 0, normalized size = 0.00 \[ \int \sqrt {-x +1}\, \sqrt {x}\, F \relax (x )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(x)*(-x+1)^(1/2)*x^(1/2),x)

[Out]

int(F(x)*(-x+1)^(1/2)*x^(1/2),x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {x} \sqrt {-x + 1} F\relax (x)\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x)*(1-x)^(1/2)*x^(1/2),x, algorithm="maxima")

[Out]

integrate(sqrt(x)*sqrt(-x + 1)*F(x), x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \sqrt {x}\,F\relax (x)\,\sqrt {1-x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^(1/2)*F(x)*(1 - x)^(1/2),x)

[Out]

int(x^(1/2)*F(x)*(1 - x)^(1/2), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {x} \sqrt {1 - x} F{\relax (x )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F(x)*(1-x)**(1/2)*x**(1/2),x)

[Out]

Integral(sqrt(x)*sqrt(1 - x)*F(x), x)

________________________________________________________________________________________