Question

What is the improper integrals 1/((8x^2)+(1)) from 0 to infinity ?

Answer 1

The integral is convergent and evaluates to approximately `0.555`

Explanation:

There is a formula for integration where

`int 1/(ax^2 + 1)dx = 1/sqrt(a) arctan(ax)`

This

`int 1/(8x^2 + 1) dx = 1/sqrt(8)arctan(sqrt(8)x)`

Now we set up the bounds

`I = lim_(t-> oo) [1/sqrt(8)arctan(sqrt(8)x)]_0^t`

`I = pi/(4sqrt(2))`

`I ~~ 0.555`

Hopefully this helps!