3.149 \(\int \frac{x}{\sqrt{3-x^2}} \, dx\)

Optimal. Leaf size=13 \[ -\sqrt{3-x^2} \]

[Out]

-Sqrt[3 - x^2]

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Rubi [A]  time = 0.00621599, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\sqrt{3-x^2} \]

Antiderivative was successfully verified.

[In]  Int[x/Sqrt[3 - x^2],x]

[Out]

-Sqrt[3 - x^2]

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Rubi in Sympy [A]  time = 0.87586, size = 8, normalized size = 0.62 \[ - \sqrt{- x^{2} + 3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x/(-x**2+3)**(1/2),x)

[Out]

-sqrt(-x**2 + 3)

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Mathematica [A]  time = 0.00259858, size = 13, normalized size = 1. \[ -\sqrt{3-x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[x/Sqrt[3 - x^2],x]

[Out]

-Sqrt[3 - x^2]

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Maple [A]  time = 0.004, size = 12, normalized size = 0.9 \[ -\sqrt{-{x}^{2}+3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(-x^2+3)^(1/2),x)

[Out]

-(-x^2+3)^(1/2)

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Maxima [A]  time = 1.33796, size = 15, normalized size = 1.15 \[ -\sqrt{-x^{2} + 3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/sqrt(-x^2 + 3),x, algorithm="maxima")

[Out]

-sqrt(-x^2 + 3)

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Fricas [A]  time = 0.207814, size = 15, normalized size = 1.15 \[ -\sqrt{-x^{2} + 3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/sqrt(-x^2 + 3),x, algorithm="fricas")

[Out]

-sqrt(-x^2 + 3)

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Sympy [A]  time = 0.151469, size = 8, normalized size = 0.62 \[ - \sqrt{- x^{2} + 3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(-x**2+3)**(1/2),x)

[Out]

-sqrt(-x**2 + 3)

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GIAC/XCAS [A]  time = 0.214832, size = 15, normalized size = 1.15 \[ -\sqrt{-x^{2} + 3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/sqrt(-x^2 + 3),x, algorithm="giac")

[Out]

-sqrt(-x^2 + 3)