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integral help, equation below

Mathematics
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\[\int\limits_{}^{}e ^{2\Theta}\sin(3\Theta)d \Theta \] that e is the to the power of 2 theta
Integration by parts to the aid.
Ugh. This one is really hard to explain. One round of integration by parts doesn't cut it. Only after two rounds of integration by parts can you get an answer. Just do two rounds of integration byparts. Then you will see that your integral in your SECOND time of ibp is the SAME integral as the one you started with times some constant. With this, you can add or subtract it back to the left hand side and then divide out.

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i got so far as to thinking it was going to be one of those integrals that has the repeated original equation within the integration by parts but there is a -1/6 in front of it and i don't know how to get rid of it without it getting messy
did i maybe do it wrong? or is there supposed to be a -1/6 in front of the repeated original equation?
You're right. Like I said before, you probably have some constant multiplied with it. It's the very same integral right? So what do you do if you have a = b + c + d + a/2 and you need to solve for a? I'd subtract a/2 from both sides: a/2 = b + c + d and get a = 2(b+c+d) Here, your integral is a!
oh geez i feel dumb = (
No worries. In college classes, people don't see it either! Actually, most don't even get to your point in solving the equation haha.
that's how it is for me most of the time lol

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