- #1

paxprobellum

- 25

- 0

**"Creative" integration by parts**

## Homework Statement

Evaluate [tex]I=\int_{0}^{Inf}e^{-kw^{2}t}cos(wx)dw[/tex] in the following way. Determine (partial derivative) dI/dx, then integrate by parts.

## Homework Equations

[tex]\int udV = uv - \int vdU[/tex]

## The Attempt at a Solution

So I have to figure out dI/dx first. I think it should be a function that lends hand to integration by parts. Obviously it has a trig portion and possibly an exponential/algebraic component. I'm a little sketchy on the details of extracting dI/dx from that equation though. My guess is:

dI/dx = (1/x)*coswx

so

[tex]I = \int (1/x)*cos(wx)dx[/tex]

Integration by parts [ u=1/x, dv = cos(wx)dx ] and I get:

[tex] (1/xw)sin(wx)+(1/w) \int (1/x^2)sin(wx)dx [/tex]

which doesn't seem to be heading in the right direction. Any thoughts?