I've tried simplifying the equation first but got stucked instead, and tried substitution also.
Which method should i use for this?
Thanks in advance.
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
At my university, students are taught general methods for the integrals and . The substitution depends on whether n and m are even or odd - it's actually pretty straightforward if you look at the derivatives of those four trigonometric functions.