I'm trying to solve the following integral

int_0^{+infintity} 1/(1+a^2*x^2)*exp(-b^2*x^2)*cos(c*x) dx

where a,b and c are real.

thanks a lot

Marco

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- July 13th 2008, 06:00 PMmathmarcointegral cosine and exponential
I'm trying to solve the following integral

int_0^{+infintity} 1/(1+a^2*x^2)*exp(-b^2*x^2)*cos(c*x) dx

where a,b and c are real.

thanks a lot

Marco - July 13th 2008, 06:03 PMMathstud28
- July 13th 2008, 09:53 PMmathmarco
yes, it is exactly that.

I will use \math next time - July 13th 2008, 09:59 PMMathstud28
- July 13th 2008, 10:22 PMmathmarco
I though it was not necessary to have

It is not sufficient that

why do you think it will diverge? Does not the following integral converge?

I'm maybe missing something... - July 13th 2008, 11:00 PMMathstud28
- July 14th 2008, 05:35 PMmathmarco
ok... good. I'm still trying to solve it but I always end up to nothing good!!

- July 14th 2008, 05:52 PMMathstud28
I can do little more than show it converges, are you sure it is integralbe? Have you tried differentiation under the integral sign after a sub of ?

So

Or in other words

and obviously since

Now

Let

So

And

and

So we have

Therefore

So we can finally conclude that

Furthermore we see that

Hope this has been some help.