Question

What is the antiderivative of `cos^2 x`?

Answer 1

`x/2+1/4sin2x+C`

Explanation:

Recall the cosine power reduction formula,

`cos^2x=1/2(1+cos2x)`

Then,

`intcos^2xdx=1/2int(1+cos2xdx)=1/2(intdx+intcos2xdx)`

`=1/2(x+1/2sin2x+C)=x/2+1/4sin2x+C`