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

Optimal. Leaf size=15 \[ -\frac{2 \sqrt{1-a x}}{a} \]

[Out]

(-2*Sqrt[1 - a*x])/a

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Rubi [A]  time = 0.00895376, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{2 \sqrt{1-a x}}{a} \]

Antiderivative was successfully verified.

[In]  Int[1/Sqrt[1 - a*x],x]

[Out]

(-2*Sqrt[1 - a*x])/a

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Rubi in Sympy [A]  time = 0.668796, size = 12, normalized size = 0.8 \[ - \frac{2 \sqrt{- a x + 1}}{a} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*sqrt(-a*x + 1)/a

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Mathematica [A]  time = 0.00485158, size = 15, normalized size = 1. \[ -\frac{2 \sqrt{1-a x}}{a} \]

Antiderivative was successfully verified.

[In]  Integrate[1/Sqrt[1 - a*x],x]

[Out]

(-2*Sqrt[1 - a*x])/a

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Maple [A]  time = 0.004, size = 14, normalized size = 0.9 \[ -2\,{\frac{\sqrt{-ax+1}}{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(-a*x+1)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.36485, size = 18, normalized size = 1.2 \[ -\frac{2 \, \sqrt{-a x + 1}}{a} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*sqrt(-a*x + 1)/a

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Fricas [A]  time = 0.205924, size = 18, normalized size = 1.2 \[ -\frac{2 \, \sqrt{-a x + 1}}{a} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*sqrt(-a*x + 1)/a

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Sympy [A]  time = 0.038173, size = 12, normalized size = 0.8 \[ - \frac{2 \sqrt{- a x + 1}}{a} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(-a*x+1)**(1/2),x)

[Out]

-2*sqrt(-a*x + 1)/a

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GIAC/XCAS [A]  time = 0.199346, size = 18, normalized size = 1.2 \[ -\frac{2 \, \sqrt{-a x + 1}}{a} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2*sqrt(-a*x + 1)/a