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

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

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

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

π

Decimal Notation

3.14159 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= π - 0

Simplify

= π

\frac{d}{d x} (tan (e^{x}))

n = 1 \sum \infty (- 1)^{n} n x^{n}

f (x) = \frac{8 x ^{2} + 6 x + 4}{x}

\frac{d y}{d t} = t 1 - y^{2}

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