Question

derivative of negative cos?

Answer 1

Do you know what the derivative of a regular cosx turns into?

Answer 2

d/dx -cos(x)=sin(x)

Answer 3

\[ \int\limits \sin(1-x) (2-\cos (1-x))^{4} dx\]

Answer 4

I would recommend using substitution for this problem.
Let u=-cos(1-x)
du=sin(1-x)dx
like how mah1 said. Then this will make your integral easier to deal with.