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

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

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

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

\frac{2 π}{3 3}

Decimal

1.20919 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{3} - \frac{π}{3 3}

Simplify

= \frac{2 π}{3 3}

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