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Ampere's Law: Magnetic field from a wire

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Consider a straight section of wire of length L which carries a current I, as shown below. Show that the magnetic field at a point P a distance R from the wire along its perpendicular bisector is B = (muI/2piR) * L/(L^2 + 4R^2)^1/2

^
: :
: :
L/2 : I :
:
: R
:-------------------->P
:
L/2 :
:
:

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See the attached file for full calculations.

:C(by letting dx be at C)
:
:L/2
:
:.............................P
O R

The angle (pi-theta) ...

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