What is the integral from 0 to infinity of 1/(4+x^2) ?

The integral from 0 to infinity of 1/(4+x^2) is pi/4

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integral from 0 to infinity of 1/(4+x^2)

\int_{0}^{\infty} \frac{1}{4 + x ^{2}} d x

\frac{π}{4}

Decimal Notation

0.78539 \dots

Solution steps

\int_{0}^{\infty} \frac{1}{4 + x ^{2}} d x

Compute the indefinite integral:

\int \frac{1}{4 + x ^{2}} d x = \frac{1}{2} arctan (\frac{x}{2}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{1}{4 + x ^{2}} d x = \frac{π}{4} - 0

= \frac{π}{4} - 0

Simplify

= \frac{π}{4}

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What is the integral from 0 to infinity of 1/(4+x^2) ?
The integral from 0 to infinity of 1/(4+x^2) is pi/4