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How do you integrate e^2x sin(3x)dx?

Mathematics
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Use integration by parts. Btw when is this due?
its a revision, we cant figure it out
No i just meant i have to do my own hw too, so do u need this like right away or by tonite or by 2morro mornin?

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Other answers:

ill just do it now
we would just like to know what to do with the sin(3x)
thanks!
ima write this out on paper and email it to u. what's ur email?
moca341@hotmail.com .. thank you :)
np
almost done...
great!
i will take separate pix and email them one by one, the whole solution won't fit lol
thats fine! haha
okay emailed it
ask me if u have any questions, either here or by email and Fan if I helped!
did u get it?
It helped a lot, but i dont really get it!, ill try to figure it out! thanks a lot!
no, ask me which part don't you understand?
I think it might the place where I let that one integral be capital i
i dont even understand the first line, dont worry about it!
Oh okay so first I used integration by parts. See the stuff in the circle: I said Let u = e^(2x), then what is du/dx? du/dx = derivative of u = 2e^(2x), multiply both sides by dx to get: du = 2e^(2x)dx
i dont see where the 1/3 cos (3x) comes from
Oh okay that's just the integral of Sin(3x)
I will work it out here: After that I said let dv/dx = Sin(3x), well then what's V? v is the integral of dv/dx with respect to x. V = Integral(dv/dx, dx) \[v = \int\limits_{}^{}Sin(3x)dx\]
Here you have to use a simple substitution: Let a = 3x; then da = 3 dx. Now you have 3x in your integral, but you still need a 3 in front of dx. To do so, multiply and divide by 3, same as multiplying by 1
ok, i get it, thanks a lot!
\[v = \int\limits_{}^{}Sin(3x)*(3/3)*dx = (1/3) *\int\limits_{}^{}Sin(3x)*3*dx\]
Now you have both a and da; your integral simplifies to: \[(1/3)\int\limits_{}^{}Sin(a)*da\]
that's it then integrate as u would a regular sin and in the end replace a by 3x

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