Electric Field off the end of a Rod

[xaer04]

Homework Statement

"A thin rod carries a total charge Q distributed uniformly over its length, L. Use integration to show that the electric field strength a distance x along the rod's direction from either end of the rod is
$$E=\frac{kQ}{\left[ x(x+L) \right]}$$."

Homework Equations

$$E = \int dE = \int \frac{k dq}{r^2}$$

The Attempt at a Solution

Somehow the $r^2$ on the bottom turns into an $x(x+L)$ AND the dq turns into a Q. I really don't understand how they integrated this problem.

 

[Doc Al]

Draw yourself a diagram and define a variable that will represent the position of the charge element dq. (I'll call it "y".) Then to convert your generic expression into one specific to this problem:
(1) express dq in terms of dy (hint: what's the charge per unit length?)
(2) express the distance between dq and the point in question (hint: this will involve L, x, and y)

Once you've done that, integrate with respect to y over the length of the rod. Only then will you get the result you're looking for.