Здравствуйте. Помогите, пожалуйста, найти интеграл
int sin^3 x/cos^7 x dx

int sin^3 x/cos^7 x dx = int sin^2 x/cos^7 x * sin x dx =
= int sin^2 x/cos^7 x d(-cos x) = -int (1 - cos^2 x)/cos^7 x d(cos x) =
= | cos x = t | = -int (1 - t^2)/t^7 dt = -int 1/t^7 dt + int 1/t^5 dt =
= -int t^(-7) dt + int t^(-5) dt = -1/(-7 + 1) * t^(-7 + 1) + 1/(-5 + 1) * t^(-5 + 1) + C =
= 1/6 * t^(-6) - 1/4 * t^(-4) + C = 1/6 * 1/t^6 - 1/4 * 1/t^4 + C =
= | t = cos x | = 1/6 * 1/cos^6 x - 1/4 * 1/cos^4 x + C