could someone show me how to take the anti derivative of

cos^2

which is also

1/2 +1/2*cos(2x)

I know that the answer is: x/2 + [sin(2x)]/4

but I'm having problems seeing the inbetween steps.

Thanks

The integral (w.r.t x) of a constant is just the constant times x. This is how 1/2 integrated over x becomes x/2. The integral of cosine is sine. Instead of being divided by 2, it is over 4 due to the chain rule (Divide by derivative of 2x).