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Math Help - Proof needed for an inequality involving definite integrals

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    Proof needed for an inequality involving definite integrals

    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
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