Solving Fourier Transform of f(x)=1/(x^2+6x+13)

saxen
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Homework Statement


Hi y'all, ran into some trouble with a Fourier transform

Im supposed to find the Fourier transform of

f(x)=\frac{1}{x^{2}+6x+13}


Homework Equations



Not that I know

The Attempt at a Solution



I tried integrating this with no luck.

All help is as usual very much appreciated!
 
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What are your thoughts on how to do the integration?
 
vela said:
What are your thoughts on how to do the integration?

Sorry, but I don't understand what you mean. Do you mean how I technically evaluate it?
 
What I'm getting at is the rules of the forum say you need to show a serious attempt at doing the problem yourself. Simply saying "I tried but couldn't figure it out" doesn't cut it.
 
vela said:
What I'm getting at is the rules of the forum say you need to show a serious attempt at doing the problem yourself. Simply saying "I tried but couldn't figure it out" doesn't cut it.

Well then, not much else to then lock thread I guess. Will call a friend instead. Thank you for reading though.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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