Помогите, пожалуйста, найти интеграл
int sin^5 x/cos^6 x dx

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

Спасибо