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 = 0.0021519, 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, Rules used = {261} \[ -\sqrt{3-x^2} \]

Antiderivative was successfully verified.

[In]

Int[x/Sqrt[3 - x^2],x]

[Out]

-Sqrt[3 - x^2]

Rule 261

Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(a + b*x^n)^(p + 1)/(b*n*(p + 1)), x] /; FreeQ
[{a, b, m, n, p}, x] && EqQ[m, n - 1] && NeQ[p, -1]

Rubi steps

\begin{align*} \int \frac{x}{\sqrt{3-x^2}} \, dx &=-\sqrt{3-x^2}\\ \end{align*}

Mathematica [A]  time = 0.0014776, 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 = 0.002, size = 12, normalized size = 0.9 \begin{align*} -\sqrt{-{x}^{2}+3} \end{align*}

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 = 0.927835, size = 15, normalized size = 1.15 \begin{align*} -\sqrt{-x^{2} + 3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(-x^2+3)^(1/2),x, algorithm="maxima")

[Out]

-sqrt(-x^2 + 3)

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Fricas [A]  time = 1.0625, size = 23, normalized size = 1.77 \begin{align*} -\sqrt{-x^{2} + 3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(-x^2+3)^(1/2),x, algorithm="fricas")

[Out]

-sqrt(-x^2 + 3)

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Sympy [A]  time = 0.142602, size = 8, normalized size = 0.62 \begin{align*} - \sqrt{3 - x^{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(-x**2+3)**(1/2),x)

[Out]

-sqrt(3 - x**2)

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Giac [A]  time = 1.09733, size = 15, normalized size = 1.15 \begin{align*} -\sqrt{-x^{2} + 3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(-x^2+3)^(1/2),x, algorithm="giac")

[Out]

-sqrt(-x^2 + 3)