Field at a distance 'z' from a solenoid

[Dell]

given a long solenoid, with a radius of R (R<<L), a current of I flows through it. find the magnetic field at point A which is located at a distance of R from the solenoid on the solenoids line of symetry.

HOW DO I DO THIS??

the only thing i see that i think i need to do here is somehow use either biot savar or more likely ampere and solve it, but how?
the only problems i have had with solenoid were to find the field inside of it in which case i took a closed loop integral and used amperes law to get B=μNI/L=μnI

what i think i need to do(but have not managed) is use biot savar, and say that the total field can only be on the 'z' axis, along the centre of the the solenoid- since the rest cancel out due to symetry,

db=(μi/4pi)*dl/L^2
using pythagarus +++> L=sqrt(r^2+Z^2) while z is constant and r goes from 0 to R

z=R

after my integration i get (μi/sqrt(32)pi)*1/R^2

 

[Dell]

what i have been told i need to do is 2 integrations, one over one coil and the second over the distance, from R to infinity, taking inot account the contributions from all the coils,

but i have not managed to get this integration right,,,