Hi i'm lookin for the integral of t*exp(-abs(t))sin(wt) dt with limits at +infinity and -infinity

Anyone available to help?

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- May 28th 2008, 11:08 AMbcvw85Find integral for this
Hi i'm lookin for the integral of t*exp(-abs(t))sin(wt) dt with limits at +infinity and -infinity

Anyone available to help? - May 28th 2008, 11:29 AMLeslon
Well, I have a solution but no steps..

I hope this will help you though.

Greets,Leslon - May 28th 2008, 11:46 AMflyingsquirrel
- May 28th 2008, 11:50 AMCaptainBlack
You are making hard work of this, see the other thread

RonL - May 28th 2008, 11:59 AMChris L T521

Write it as two separate integrals:

Apply integration by parts:

let and

Therefore, and (you get v by using integration by parts...again... :(

Plugging into the integration by parts formula:

Before we move on, note that converges to 0.

Thus, we have left:

Apply integration by parts (again) for these two integals:

I will leave steps out, hoping that you can do it on your own.

Now, the integrals should become

Since we only evaluated half of the integral, double it to get the answer:

Hope that this made sense!! :D