Math Help - comparison test for improper intgral

1. comparison test for improper intgral

hi!
can someone tell me how do you choose the second function .
thanks .

integral sin ^2 x /2x^2 -1 dx from 1 to infinity .

2. Does the integral $\int_1^\infty {\frac{1}{{2x^2 - 1}}dx}$ converge?