3.547 \(\int \frac{x}{\sqrt{9-4 x^2}} \, dx\)

Optimal. Leaf size=15 \[ -\frac{1}{4} \sqrt{9-4 x^2} \]

[Out]

-Sqrt[9 - 4*x^2]/4

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Rubi [A]  time = 0.00878129, antiderivative size = 15, 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 \[ -\frac{1}{4} \sqrt{9-4 x^2} \]

Antiderivative was successfully verified.

[In]  Int[x/Sqrt[9 - 4*x^2],x]

[Out]

-Sqrt[9 - 4*x^2]/4

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Rubi in Sympy [A]  time = 2.00313, size = 12, normalized size = 0.8 \[ - \frac{\sqrt{- 4 x^{2} + 9}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x/(-4*x**2+9)**(1/2),x)

[Out]

-sqrt(-4*x**2 + 9)/4

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Mathematica [A]  time = 0.00295312, size = 15, normalized size = 1. \[ -\frac{1}{4} \sqrt{9-4 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[x/Sqrt[9 - 4*x^2],x]

[Out]

-Sqrt[9 - 4*x^2]/4

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Maple [A]  time = 0.004, size = 22, normalized size = 1.5 \[{\frac{ \left ( 2\,x-3 \right ) \left ( 2\,x+3 \right ) }{4}{\frac{1}{\sqrt{-4\,{x}^{2}+9}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(-4*x^2+9)^(1/2),x)

[Out]

1/4*(2*x-3)*(2*x+3)/(-4*x^2+9)^(1/2)

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Maxima [A]  time = 1.35076, size = 15, normalized size = 1. \[ -\frac{1}{4} \, \sqrt{-4 \, x^{2} + 9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/sqrt(-4*x^2 + 9),x, algorithm="maxima")

[Out]

-1/4*sqrt(-4*x^2 + 9)

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Fricas [A]  time = 0.236573, size = 23, normalized size = 1.53 \[ \frac{x^{2}}{\sqrt{-4 \, x^{2} + 9} - 3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/sqrt(-4*x^2 + 9),x, algorithm="fricas")

[Out]

x^2/(sqrt(-4*x^2 + 9) - 3)

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Sympy [A]  time = 0.323522, size = 12, normalized size = 0.8 \[ - \frac{\sqrt{- 4 x^{2} + 9}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(-4*x**2+9)**(1/2),x)

[Out]

-sqrt(-4*x**2 + 9)/4

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GIAC/XCAS [A]  time = 0.207186, size = 15, normalized size = 1. \[ -\frac{1}{4} \, \sqrt{-4 \, x^{2} + 9} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/sqrt(-4*x^2 + 9),x, algorithm="giac")

[Out]

-1/4*sqrt(-4*x^2 + 9)