Magnetic field of an infinite wire

[asi123]

Homework Statement

Hey guys.
So I've got a current which goes through an infinite wire and I need to find the magnetic field which is caused by the wire at point P.
I used the Biot–Savart Law and in the picture you can see what I came up with (sorry, no scanner today, I had to do it the short way ).
So, my question is, how am I suppose to get from the green equation to the red one? I took the red equation from their answers.
Am I missing something?

Thanks.

Homework Equations

The Attempt at a Solution

 

[Hootenanny]

You might want to recheck the Green equation, it seems that you did not integrate correctly.

 

[asi123]

You might want to recheck the Green equation, it seems that you did not integrate correctly.

Ops, my bag, how am I suppose to integrate it?

 

[Hootenanny]

Ops, my bag, how am I suppose to integrate it?

No problem. That integral looks almost like a standard integral and can be evaluated using the same substitution as you would use for the standard integral...