How do I integrate (e^ax)sin(bx)
I think integration by parts will work.
A somewhat clumsy, but direct, method is to use the representation of sin(bx) in terms of exp. Specifically:
sin(bx)=(e^ibx - e^-ibx)/2i
This gives you two integrals of the exp function. You can then do a little playing around to get rid of the i terms.
Integration by parts will work, but there's a bit more to it. You will need to apply integration by parts twice. After the second application, a multiple of your original integral will reappear. You would then have to isolate this integral. In other words, you will obtain something like:
I = (stuff from using integration by parts twice) + a*I
where 'I' represents your original integral and 'a' is some constant. You'd then have to "solve" for the 'I'
I just thought I'd add this because oftentimes students only apply integration by parts once and do not see the solution right away, and get flustered.
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