Your answer is correct. It's probably a typo in the book.
A problem in my calc. book asks to integrate [4 sin x + 2 cos x].
I get: -4 cos x + 2 sin x + C
The book, however, lists the answer as: -4 cos x + sin x + C
Is the book correct? I don't understand what happens to the 2 in '2 cos x', during integration.