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

• Feb 21st 2010, 06:45 PM
s3a
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.)

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.
• Feb 21st 2010, 07:55 PM
Prove It
Quote:

Originally Posted by s3a
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.)

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.

If you use integration by parts again on your new integral, you will end up with an equation in $\displaystyle \int{e^{2\theta}\sin{3\theta}\,d\theta}$.

Then by moving all of the integrals to one side, you can solve for the integral.
• Feb 21st 2010, 07:55 PM
Shananay
Keep going until you get your original integral back on the right side. Subtract that integral from both sides and divide.
• Feb 21st 2010, 07:57 PM
ione
Quote:

Originally Posted by s3a
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.)

Use integration by parts again to intgrate $\displaystyle \int{e^{2\theta}\cos{3\theta}\,d\theta}$
You will get $\displaystyle \int{e^{2\theta}\sin{3\theta}\,d\theta}$ appearing again.