Question

How do I tell if this converges or diverges? Im not sure how to do this integral, or if I even need to to determine that

Answer 1

\[\int\limits_{1}^{\inf}\frac{ 2+\cos(x)}{ x^2 } dx\]\]

Answer 2

Judging by answers to similar problems I should be comparing it to a simpler similar integral whos convergence is known.. I am not sure how to determine what that similar expression is.

Answer 3

I would use the fact that\[\cos x\le1\] and rewrite a larger integrand replacing cosx with 1

Answer 4

you know (hopefully) that\[\int_1^\infty\frac1{x^2}dx\]converges