How to integrate K/[(y^2 + K)^3/2] dy

[animboy]

As you can see the function given is

K/[(y² + K)^1.5]

The integral of this equation with respect to dy is part of the explanation my textbook gives of finding electric field due to line of uniformly charged wire, where y of course is the variable length of the wire. Then it gives the integral as

y/[d(y² + k²)^0.5]

but I can't see how it got this, since I try to differentiate this answer and got back this function which was different to the original.

Can someone whow me how the textbook got that answer? Thanks.
This function is radically different

Here is a picture of the original textbook statement.

[PLAIN]http://desmond.imageshack.us/Himg97/scaled.php?server=97&filename=physicsq.png&res=medium

 

[Rayquesto]

integrate ((y^2 + K)^-3/2)dy=dv to get -((y^2 + K)^-1/2)/y=v

then

multiply that times K and you should be able to get the right answer since K is constant right?

this is just what I think

 

[animboy]

Never mind, I found out what I did wrong. I misused the product rule. What a simple mistake.