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Integrating Trigometric functions times e^x by parts

say we have a question

integrate exsin2xe^xsin2x

how do we go about doing this, seen as we cant integrate or differentiate to remove either term?
Reply 1
Avatar for nicknick
nicknick
You could try using the identity sin⁡x=eix−e−ix2i\sin x = \dfrac {e^{ix} - e^{-ix}}{2i}
Reply 2
Avatar for DFranklin
DFranklin
18
ziigmund
say we have a question

integrate exsin2xe^xsin2x

how do we go about doing this, seen as we cant integrate or differentiate to remove either term?
Do it twice; if I=∫exsin⁡2x dxI = \int e^x \sin 2x\,dx, you end up with something like I = {stuff} - 4I, and so you can deduce 5I = {stuff}.

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