What is the integral from 1 to infinity of 1/(x^2+3) ?

The integral from 1 to infinity of 1/(x^2+3) is pi/(3sqrt(3))

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integral from 1 to infinity of 1/(x^2+3)

\int_{1}^{\infty} \frac{1}{x ^{2} + 3} d x

\frac{π}{3 3}

Decimal

0.60459 \dots

Solution steps

\int_{1}^{\infty} \frac{1}{x ^{2} + 3} d x

Compute the indefinite integral:

\int \frac{1}{x ^{2} + 3} d x = \frac{1}{3} arctan (\frac{x}{3}) + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{x ^{2} + 3} d x = \frac{π}{2 3} - \frac{π}{6 3}

= \frac{π}{2 3} - \frac{π}{6 3}

Simplify

= \frac{π}{3 3}

y = 3 1.6 x^{2} + 4.9

f (t) = \frac{1}{2} (9 t^{2} + t)^{- 3}

x \to \infty lim (2 1^{x})

\frac{\partial}{\partial y} (cos (12 x) sin (2 y))

\int \frac{9}{x ln ( 3 x )} d x

What is the integral from 1 to infinity of 1/(x^2+3) ?
The integral from 1 to infinity of 1/(x^2+3) is pi/(3sqrt(3))