3.10.4 \(\int \frac {F(x)}{\sqrt {1-x} \sqrt {x}} \, dx\) [904]

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

[Out]

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

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Rubi [A]
time = 0.08, 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 \frac {F(x)}{\sqrt {1-x} \sqrt {x}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[F[x]/(Sqrt[1 - x]*Sqrt[x]),x]

[Out]

Defer[Int][F[x]/Sqrt[x - x^2], x]

Rubi steps

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

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

Verification is not applicable to the result.

[In]

Integrate[F[x]/(Sqrt[1 - x]*Sqrt[x]),x]

[Out]

Integrate[F[x]/(Sqrt[1 - x]*Sqrt[x]), x]

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

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

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(F(x)/(x^(1/2)*(1 - x)^(1/2)),x)

[Out]

int(F(x)/(x^(1/2)*(1 - x)^(1/2)), x)

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