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

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

[Out]

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

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, 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*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \[ -\sqrt {3-x^2} \]

Antiderivative was successfully verified.

[In]

Integrate[x/Sqrt[3 - x^2],x]

[Out]

-Sqrt[3 - x^2]

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fricas [A]  time = 0.41, size = 11, normalized size = 0.85 \[ -\sqrt {-x^{2} + 3} \]

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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giac [A]  time = 0.01, size = 11, normalized size = 0.85 \[ -\sqrt {-x^{2} + 3} \]

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)

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maple [A]  time = 0.00, size = 12, normalized size = 0.92 \[ -\sqrt {-x^{2}+3} \]

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 = 0.48, size = 11, normalized size = 0.85 \[ -\sqrt {-x^{2} + 3} \]

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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mupad [B]  time = 0.17, size = 11, normalized size = 0.85 \[ -\sqrt {3-x^2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/(3 - x^2)^(1/2),x)

[Out]

-(3 - x^2)^(1/2)

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sympy [A]  time = 0.15, size = 8, normalized size = 0.62 \[ - \sqrt {3 - x^{2}} \]

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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