Electric field due to a finite line of charge

[gboff21]

Homework Statement

A line of length 2a on the y-axis centred in the middle of the x-axis with its ends at a and -a on the y axis, has been charged with charge Q. Work out the electric field at point x on the x axis.

Homework Equations

E=kdQ/r^2
dQ=Qdy/2a

The Attempt at a Solution

I have the answer in front of me: Qk*1/(x(x^2+a^2)^1/2)

I start with dE_x= kQxdy/2a(x^2+y^2)^3/2 (added the x component with x/(x^2+y^2)^1/2)
This integral is the bit I don't understand!

How do you integrate dy/(x^2+y^2)^1/2 ?
Apparently the answer is y/(x^2(x^2+y^2)^1/2). How does this work?

And it does give the correct answer if you follow it on. But How do you integrate that?

 

[kuruman]

To do this integral, use the substitution y = x tanθ and see what you get.