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

Optimal. Leaf size=16 \[ \text{CannotIntegrate}\left (\frac{F(x)}{\sqrt{x-x^2}},x\right ) \]

[Out]

CannotIntegrate[F[x]/Sqrt[x - x^2], x]

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Rubi [A]  time = 0.112653, 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., Rules used = {} \[ \int \frac{F(x)}{\sqrt{1-x} \sqrt{x}} \, dx \]

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*}

Mathematica [A]  time = 0.0199639, size = 0, normalized size = 0. \[ \int \frac{F(x)}{\sqrt{1-x} \sqrt{x}} \, dx \]

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 = 0.015, size = 0, normalized size = 0. \begin{align*} \int{F \left ( x \right ){\frac{1}{\sqrt{1-x}}}{\frac{1}{\sqrt{x}}}}\, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \int \frac{F\left (x\right )}{\sqrt{x} \sqrt{-x + 1}}\,{d x} \end{align*}

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., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{\sqrt{x} \sqrt{-x + 1} F\left (x\right )}{x^{2} - x}, x\right ) \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \int \frac{F{\left (x \right )}}{\sqrt{x} \sqrt{1 - x}}\, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \int \frac{F\left (x\right )}{\sqrt{x} \sqrt{-x + 1}}\,{d x} \end{align*}

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)