- #1

CivilSigma

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## Homework Statement

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I am trying to determien the characteristic function of the function:

$$ f(x)= ae^{-ax}$$

$$\therefore E(e^{itx}) =\int_0^\infty e^{itx}ae^{-ax} dx = a \cdot \frac{e}{it-a} |_0 ^ \infty $$

But I am not sure how to evaluate the integral.

Wolfram alpha suggests this, but I am not sure how to get there.

https://www.wolframalpha.com/input/?i=integral+from+0+to+infitiy+of+e^(itx)*ae^(-ax)dx

## The Attempt at a Solution

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If you just plug in the limits you get (∞ - ...) which is indeterminate.

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