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This integral brings me somewhat back to where I started after Integration by parts!

After having attempted integration by parts, it only seems to make this problem harder! I tried having u = e^(2x), and as the work shows, u = sin(3x) and neither way brings me anywhere. (In the problem x = theta)

(I attached my work.)

Someone please help me!

Thanks!

P.S.

Wolfram Alpha shows something beyond my understanding: http://www.wolframalpha.com/input/?i=integral+e^(2x)+*+sin(3x)

P.P.S

I am getting really scared because I tried to advance in my homework but the following problem seems to be similar to this one and if I can't do this one then I can't advance! I will still attempt it however, while someone answers this question here.