Question

what is the indefinite integral of the function:

f(x)=sin^2 (1/8 * x)
in stages if possible
thanks

Answer 1

Let x/8 = u

dx = 8 du
So you want the integral of
8*sin^2 u du
sin^2 u = (1/2)[1 - cos(2u)]
=> integral of 4[1 - cos(2u)] du
Let w = 2u; du = dw/2
= 4u - 2 sin(w)
= x/2 - 2 sin(2u) = x/2 - 2sin(x/4)

Check my thinking. I tend to be sloppy