Answer
$\sin x + \cos x +C$
Work Step by Step
We need to simplify: $\int (\cos x - \sin x ) \ dx $
Separate the integrals.
$ \int (\cos x - \sin x ) \ dx=\int \cos x \ dx - \int \sin x \ dx$
or, $\int \cos x \ dx - \int \sin x \ dx= \sin x + \cos x +C$
