3.901 \(\int \sqrt {x-x^2} F(x) \, dx\)

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)

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Rubi [A]  time = 0.03, 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 = {} \[ \int \sqrt {x-x^2} F(x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sqrt[x - x^2]*F[x],x]

[Out]

Defer[Int][Sqrt[x - x^2]*F[x], x]

Rubi steps

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

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Mathematica [A]  time = 0.10, size = 0, normalized size = 0.00 \[ \int \sqrt {x-x^2} F(x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sqrt[x - x^2]*F[x],x]

[Out]

Integrate[Sqrt[x - x^2]*F[x], x]

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fricas [A]  time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\sqrt {-x^{2} + x} F\relax (x), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(sqrt(-x^2 + x)*F(x), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {-x^{2} + x} F\relax (x)\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(sqrt(-x^2 + x)*F(x), x)

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maple [A]  time = 0.07, size = 0, normalized size = 0.00 \[ \int \sqrt {-x^{2}+x}\, F \relax (x )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {-x^{2} + x} F\relax (x)\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(sqrt(-x^2 + x)*F(x), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int F\relax (x)\,\sqrt {x-x^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(x)*(x - x^2)^(1/2),x)

[Out]

int(F(x)*(x - x^2)^(1/2), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(sqrt(-x*(x - 1))*F(x), x)

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