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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

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