# C4 Integration by parts questioWatch

#1
Hi, could someone show me the workings for this integration

e^(2x)sin(2x)

I think it's integrated by parts twice, but I just find myself going in circles!

Thanks
0
4 years ago
#2
(Original post by Youk)
Hi, could someone show me the workings for this integration

e^(2x)sin(2x)

I think it's integrated by parts twice, but I just find myself going in circles!

Thanks
There's a trick to it. Call the integral I. After you have integrated by parts twice you obtain I again so it appears on both sides of your equation. Now simplify.
1
4 years ago
#3
You'll get your original integral again.

Let that equal I.

Solve for I.

Voila!
1
4 years ago
#4
(Original post by Youk)
Hi, could someone show me the workings for this integration

e^(2x)sin(2x)

I think it's integrated by parts twice, but I just find myself going in circles!

Thanks
Let

Your first IBP should look something like:

Now, integrate again, and you should get back to your first integral, or

I've put my answer in the spoiler, check it once you've attempted it

Spoiler:
Show
1
#5
(Original post by CTArsenal)
Let

Your first IBP should look something like:

Now, integrate again, and you should get back to your first integral, or

I've put my answer in the spoiler, check it once you've attempted it

Spoiler:
Show
Thank you all for the help, just a correction for anyone looking at this in the future, the first IBP looks like

0
4 years ago
#6
Neither is wrong. You just chose to differentiate and integrate the reverse parts.

Good luck.
0
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