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