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

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

[Out]

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

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Rubi [A]  time = 0.19041, 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. \[ \text{Int}\left (\frac{F(x)}{\sqrt{1-x} \sqrt{x}},x\right ) \]

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]

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Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ 2 \int ^{\sqrt{x}} \frac{F{\left (x^{2} \right )}}{\sqrt{- x^{2} + 1}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(F(x)/(1-x)**(1/2)/x**(1/2),x)

[Out]

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

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Mathematica [A]  time = 0.0329714, 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 = 0.025, size = 0, normalized size = 0. \[ \int{F \left ( x \right ){\frac{1}{\sqrt{1-x}}}{\frac{1}{\sqrt{x}}}}\, dx \]

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., size = 0, normalized size = 0. \[ \int \frac{F\left (x\right )}{\sqrt{x} \sqrt{-x + 1}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F(x)/(sqrt(x)*sqrt(-x + 1)),x, algorithm="maxima")

[Out]

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

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F(x)/(sqrt(x)*sqrt(-x + 1)),x, algorithm="fricas")

[Out]

Exception raised: TypeError

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

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(-x + 1)), x)

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GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{F\left (x\right )}{\sqrt{x} \sqrt{-x + 1}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F(x)/(sqrt(x)*sqrt(-x + 1)),x, algorithm="giac")

[Out]

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