Determine whether the series is convergent or divergent:

The sum from n=1 to infinity of the series 1/(5n+2).

I used the divergence test -- lim(n->inf) of 1/(5n+2) -> infinity, therefore, not divergent.

But if I integrate,

The integral from 1 to inf of 1/(5x+2) dx ; lim(t->inf) of the integral of 1 to t of 1/(5x+2) dx, use u substitution, etcetera, to come out with

(1/5) lim(t->inf) of ln|5t+2| - ln|7|, which is of course infinity.

? Help

Am I just not understanding something here?