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

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

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

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

\frac{π}{2}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

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