What is the integral from 0 to infinity of 2/(9+x^2) ?

The integral from 0 to infinity of 2/(9+x^2) is pi/3

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integral from 0 to infinity of 2/(9+x^2)

\int_{0}^{\infty} \frac{2}{9 + x ^{2}} d x

\frac{π}{3}

Decimal Notation

1.04719 \dots

Solution steps

\int_{0}^{\infty} \frac{2}{9 + x ^{2}} d x

Compute the indefinite integral:

\int \frac{2}{9 + x ^{2}} d x = \frac{2}{3} arctan (\frac{x}{3}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{2}{9 + x ^{2}} d x = \frac{π}{3} - 0

= \frac{π}{3} - 0

Simplify

= \frac{π}{3}

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What is the integral from 0 to infinity of 2/(9+x^2) ?
The integral from 0 to infinity of 2/(9+x^2) is pi/3