This integral is commonly used in the derivation of error probability on Rician fading channels however its detailed derivation is usually omitted.

Evaluate int_{0}^{infty}exp(-Ab^2)p(b)db, where b is a Rician random variable with the probability density function p(b)=2b(1+K)exp(-K-b^2(1+K))I_0(2bsqrt(K(1+K))), b>=0, p(b) = 0, b<0, where K is a constant and I_0(.) is the zero-order modified Bessel function of the first kind.