3.120 \(\int \frac{x}{\sqrt{4+x^2}} \, dx\)

Optimal. Leaf size=9 \[ \sqrt{x^2+4} \]

[Out]

Sqrt[4 + x^2]

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Rubi [A]  time = 0.00466439, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \sqrt{x^2+4} \]

Antiderivative was successfully verified.

[In]  Int[x/Sqrt[4 + x^2],x]

[Out]

Sqrt[4 + x^2]

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Rubi in Sympy [A]  time = 0.761721, size = 7, normalized size = 0.78 \[ \sqrt{x^{2} + 4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(x**2 + 4)

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Mathematica [A]  time = 0.00133305, size = 9, normalized size = 1. \[ \sqrt{x^2+4} \]

Antiderivative was successfully verified.

[In]  Integrate[x/Sqrt[4 + x^2],x]

[Out]

Sqrt[4 + x^2]

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Maple [A]  time = 0.004, size = 8, normalized size = 0.9 \[ \sqrt{{x}^{2}+4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(x^2+4)^(1/2),x)

[Out]

(x^2+4)^(1/2)

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Maxima [A]  time = 1.34601, size = 9, normalized size = 1. \[ \sqrt{x^{2} + 4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(x^2 + 4)

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Fricas [A]  time = 0.20864, size = 41, normalized size = 4.56 \[ -\frac{x^{2} - \sqrt{x^{2} + 4} x + 4}{x - \sqrt{x^{2} + 4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(x^2 - sqrt(x^2 + 4)*x + 4)/(x - sqrt(x^2 + 4))

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Sympy [A]  time = 0.152024, size = 7, normalized size = 0.78 \[ \sqrt{x^{2} + 4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(x**2+4)**(1/2),x)

[Out]

sqrt(x**2 + 4)

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GIAC/XCAS [A]  time = 0.200531, size = 9, normalized size = 1. \[ \sqrt{x^{2} + 4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

sqrt(x^2 + 4)