I would like to know Whether the integration
$\int_0^\infty\frac{s^{N_1+N_2}(2s^{N_1+1}-1)}{(1+s^{N_1+1})^4(1+s^{N_2+1})^2}ds$
is positive or negative? where $N_1,N_2$ are positive integers.
I am very grateful if anyone can give some ideas or solutions.