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

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

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

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

π

Decimal

3.14159 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= π - 0

Simplify

= π

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