int x/cos^4 x dx = int x * 1/cos^2 x d(tg x) =
= int x * (1 + tg^2 x) d(tg x) = | tg x = t; x = arctg t; dx=dt/(1 + t^2) | =
= int arctg t * (1+t^2) dt = int arctg t dt + int t^2 * arctg t dt
Далее по частям каждый...