What is the integral from 0 to infinity of 3/(x^2+5) ?

The integral from 0 to infinity of 3/(x^2+5) is (3pi)/(2sqrt(5))

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integral from 0 to infinity of 3/(x^2+5)

\int_{0}^{\infty} \frac{3}{x ^{2} + 5} d x

\frac{3 π}{2 5}

Decimal

2.10744 \dots

Solution steps

\int_{0}^{\infty} \frac{3}{x ^{2} + 5} d x

Compute the indefinite integral:

\int \frac{3}{x ^{2} + 5} d x = \frac{3}{5} arctan (\frac{x}{5}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{3}{x ^{2} + 5} d x = \frac{3}{5} \cdot \frac{π}{2} - 0

= \frac{3}{5} \cdot \frac{π}{2} - 0

Simplify

= \frac{3 π}{2 5}

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What is the integral from 0 to infinity of 3/(x^2+5) ?
The integral from 0 to infinity of 3/(x^2+5) is (3pi)/(2sqrt(5))