Just trying to understand the answer in my book here...
given that cos(2x) = 2cos^2 x -1
cos^2 x = 1/2(cos(2x) + 1). agreed.
my problem comes upon integrating cos^2 x..
i get thus far:
cos^2 x dx = 1/2(cos(2x) + 1).
=1/2(1/2 sin(2x) + x) + c
agreed. it is the next bit that is throwing me off..
distributing out the 1/2 i get:
1/4sin(2x) + 2x) + c
i'm sure i'm missing something terribly obvious here, but where does the the extra x (2x term) pop up from ?
kind thankyous in advance!