What is the integral from 0 to infinity of 5/(x^2+4) ?

The integral from 0 to infinity of 5/(x^2+4) is (5pi)/4

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integral from 0 to infinity of 5/(x^2+4)

\int_{0}^{\infty} \frac{5}{x ^{2} + 4} d x

\frac{5 π}{4}

Decimal Notation

3.92699 \dots

Solution steps

\int_{0}^{\infty} \frac{5}{x ^{2} + 4} d x

Compute the indefinite integral:

\int \frac{5}{x ^{2} + 4} d x = \frac{5}{2} arctan (\frac{x}{2}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{5}{x ^{2} + 4} d x = \frac{5 π}{4} - 0

= \frac{5 π}{4} - 0

Simplify

= \frac{5 π}{4}

\int cos (8 x^{2}) d x

\frac{\partial}{\partial x} (- x)

\int_{0}^{4} 2 x d x

y^{^{''}} - 4 y^{^{'}} = 7 x + 1

\frac{\partial}{\partial x} (e^{4 x} cos (7 y))

What is the integral from 0 to infinity of 5/(x^2+4) ?
The integral from 0 to infinity of 5/(x^2+4) is (5pi)/4