I'm trying to deduce weather this improper integral is convergent or not: $$ \int_{0}^{1}\dfrac{\cos(\frac{1}{x})}{x}dx. $$ I've tried using Dirichlet's test for convergence, yet I cant seem to properly 'place' the functions under the needed terms.
I was hinted by a colleague that substitution can be applied here yet I see no way of utilizing that method.
I'm not sure how to move forward at this point, hints are happily accepted!
Thanks in advance!