math

what is the indefinite integral of the function:
f(x)=sin^2 (1/8 * x)
in stages if possible
thanks

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  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

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