hmmm why don't you try to first factor sin^3(2x) to sin^2(2x)(sin(2x))... then since sin^2(2x) is also equal to 1-cos^2(2x).... you rearrange it to a indefinite integral of cos^4(2x)[1-cos^2(2x)]sin(2x)dx.. then do substitution... u=cos (2x).... du= (2)(-sin(2x))dx.... now... please do the rest