What is the integral from 0 to infinity of 3/(x^2+4) ?

The integral from 0 to infinity of 3/(x^2+4) is (3pi)/4

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integral from 0 to infinity of 3/(x^2+4)

\int_{0}^{\infty} \frac{3}{x ^{2} + 4} d x

\frac{3 π}{4}

Decimal Notation

2.35619 \dots

Solution steps

\int_{0}^{\infty} \frac{3}{x ^{2} + 4} d x

Compute the indefinite integral:

\int \frac{3}{x ^{2} + 4} d x = \frac{3}{2} arctan (\frac{x}{2}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{3}{x ^{2} + 4} d x = \frac{3 π}{4} - 0

= \frac{3 π}{4} - 0

Simplify

= \frac{3 π}{4}

x y y^{^{'}} = 2 (2 x^{2} + y^{2})

\frac{d}{d x} (\frac{tan ( 2 x ) - 1}{x ^{2}})

0.0018425 (t + 7)^{4.5}

y = x^{2} ln (2 x)

\int \frac{1 - x}{x} d x

What is the integral from 0 to infinity of 3/(x^2+4) ?
The integral from 0 to infinity of 3/(x^2+4) is (3pi)/4