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

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 = 0.04, 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 = {} \[ \int \frac {F(x)}{\sqrt {x-x^2}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[F[x]/Sqrt[x - x^2],x]

[Out]

Defer[Int][F[x]/Sqrt[x - x^2], x]

Rubi steps

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

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Mathematica [A]  time = 0.18, size = 0, normalized size = 0.00 \[ \int \frac {F(x)}{\sqrt {x-x^2}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[F[x]/Sqrt[x - x^2],x]

[Out]

Integrate[F[x]/Sqrt[x - x^2], x]

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

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^2 - x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(F(x)/sqrt(-x^2 + x), x)

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

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 \[ \int \frac {F\relax (x)}{\sqrt {-x^{2} + x}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(F(x)/sqrt(-x^2 + x), x)

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

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 \[ \int \frac {F{\relax (x )}}{\sqrt {- x \left (x - 1\right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(F(x)/sqrt(-x*(x - 1)), x)

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