Question

How do you evaluate the integral `int 1/x dx` from 1 to `oo` if it converges?

Answer 1

The integral does not converge.

Explanation:

`int_1^a 1/x dx=lna-ln1=lna`

We know that `lnx` is a strict monotonic increasing function so

`lim_(a->oo)lna=oo`. So we conclude that

`lim_(a->oo)int_1^a 1/x dx = oo` so does not converge.