Assume: b1>0, b2>0 and x>1
Define:
W(x)= int (sin(q)*(1-exp(-b1*abs(1-x*sin(q))))*(1+exp(-b2*abs(1-x*sin(q))))*sign(1-x*sin(q)), 0, 2*pi).
Prove that:
W(x)<W(1) for all x>1
Note 1: I've used "int(Y,a,b)" for definite intgration of Y from a to b.
Note 2: pdf version attached