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

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

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

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

π

Decimal

3.14159 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 2 π - π

Simplify

= π

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