3.10.3 \(\int \sqrt {1-x} \sqrt {x} F(x) \, dx\) [903]

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 = 0.07, 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 = {} \begin {gather*} \int \sqrt {1-x} \sqrt {x} F(x) \, dx \end {gather*}

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*}

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Mathematica [A]
time = 0.02, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {1-x} \sqrt {x} F(x) \, dx \end {gather*}

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]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {x} \sqrt {1 - x} F{\left (x \right )}\, dx \end {gather*}

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)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \sqrt {x}\,F\left (x\right )\,\sqrt {1-x} \,d x \end {gather*}

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)

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