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

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

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

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

π

Decimal Notation

3.14159 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= π - 0

Simplify

= π

x^{2} tan (x)

\frac{\partial}{\partial x} (ln (\frac{1}{x}))

\frac{d y}{d x} = \frac{2 y}{x}

e^{5 t}

y^{^{'}} = - 2 y + 5

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