Assuming the the posted formula is correct in having the exp() raised as an exponent to the (r/2KB) then:
Because you want to integrate to r = infinity, examine your p(r) as r increases towards infinity.
exp(-(r+2KB)/2) as r increases towards infinity heads to exp(-infinity) which head towards 0 from above.
That 0-limit is being multiplied by a constant (K-1)/2 which continues to give the 0-limit.
That 0-limit is the exponent of r/(2*K*B) and so that limit would be r^0 which would be limit-1 -- a non-zero constant
The leading 1/2 is a positive multiplicative constant, and a positive constant times a limit-constant gives a positive constant in the limit.
Thus as r goes to infinity the part of the expression before the besseli goes to positive constant.
Now, the integration of a positive constant out to infinity is infinity, so if we ignore the besseli for the moment, we see we are at risk of an infinite outcome of the integral.
When would the true integral potentially be below infinity? Only if the besseli() portion goes towards zero. But for real-valued constant nu, besseli(nu, x) increases without bound with increasing x. And sqrt(2*K*B*r) is strictly increasing in increasing r.
Therefore, if the exp() is properly part of the exponent of (r/2KB) then the integral of p as r goes to infinity is going to be infinite.
... Now if the exp() should not be part of the exponent, if it should be at the same baseline as the (r/2KB) then the analysis would be notably different.
where 
is the modified Bessel function of the first kind of order K-1. I want to integrate
from b (which is a constant I decide on) to infinity. And K and B are also constants which I decide on. This integral that I want to perform is insanely close to the Marcum-Q integral which MATLAB already has a function for (https://www.mathworks.com/help/signal/ref/marcumq.html). Unfortuantely though, I don't think its possible to use it because my 
is very slightly different. I also tried developing my own function and failed. Any help is appreciated.
