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

Optimal. Leaf size=11 \[ -2 \sqrt{1-x} \]

[Out]

-2*Sqrt[1 - x]

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Rubi [A]  time = 0.00565314, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ -2 \sqrt{1-x} \]

Antiderivative was successfully verified.

[In]  Int[1/Sqrt[1 - x],x]

[Out]

-2*Sqrt[1 - x]

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Rubi in Sympy [A]  time = 0.525788, size = 8, normalized size = 0.73 \[ - 2 \sqrt{- x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*sqrt(-x + 1)

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Mathematica [A]  time = 0.00252851, size = 11, normalized size = 1. \[ -2 \sqrt{1-x} \]

Antiderivative was successfully verified.

[In]  Integrate[1/Sqrt[1 - x],x]

[Out]

-2*Sqrt[1 - x]

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Maple [A]  time = 0.003, size = 10, normalized size = 0.9 \[ -2\,\sqrt{1-x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1-x)^(1/2),x)

[Out]

-2*(1-x)^(1/2)

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Maxima [A]  time = 0.680677, size = 12, normalized size = 1.09 \[ -2 \, \sqrt{-x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*sqrt(-x + 1)

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Fricas [A]  time = 0.265146, size = 12, normalized size = 1.09 \[ -2 \, \sqrt{-x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*sqrt(-x + 1)

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Sympy [A]  time = 0.066209, size = 8, normalized size = 0.73 \[ - 2 \sqrt{- x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(1-x)**(1/2),x)

[Out]

-2*sqrt(-x + 1)

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GIAC/XCAS [A]  time = 0.261089, size = 12, normalized size = 1.09 \[ -2 \, \sqrt{-x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*sqrt(-x + 1)