IntegrateI exapned sin4x and did some partial fractions stuff, but the answer which I get is not the back answerCode:sinx/sin4x
integrate Sin[x]/Sin[4x] - Wolfram|Alpha
Click on Show steps.
Wolfram's steps look too frightening. I'd rather go for a trigonometric substitution:
, so with a little trigonometry:
, and we have an integral of a rational function.
Indeed this still is a nasty integral, but perhaps a little less messier than in the steps of the proposed solution
in Wolfram's...perhaps.
Tonio
Wolfram also made mess of the partial fractions:
If letting gives , then simply write:
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Thus our original integral evaluates to: