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

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

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

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

\frac{π}{4}

Decimal Notation

0.78539 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{4} - 0

Simplify

= \frac{π}{4}

x^{4} e^{- x}

y = e^{2 e x}

\frac{\partial}{\partial x} (x^{3} - y^{3} + 6 x y)

\int 1 + e^{x} d x

\frac{d}{d x} (ln (x^{8} + 19))

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