My question is about this integral:

After using the substitution, u2 = tan(x), I got,

Next, I tried the partial fraction expansion. But it turned pretty ugly. Is there any easier way of doing it?

I got a partial solution

There is;

how is

integration of 2u^2/(u^4 + 1).du?

it is integration of 2u^3/(u^4 + 1)

equal to