Integral within exponential within integral

I am trying to numerically integrate a few different expressions, but they all have an integral within an exponential, surrounded by another integral, i.e.

I can't seem to get this to solve based on my code below

syms s p t

W = 3.18*10^(-22)

b = 10^(-23)

X = 300

L = 0.374

intlim = 0.589

myfuncirc = @(s,p,t) (-W).*sqrt((L.^2)-(s.^2)).*(((-p.*cos(t))+sqrt(1-((p.^2).*((sin(t)).^2)))-sqrt(L.^2-s.^2)).^(-2))

s_min = 0

s_max = L

t_min = 0

t_max = pi

integral(@(p)(p.*exp(-(integral2(@(s,t) myfuncirc(s,t,p),s_min,s_max,t_min,t_max))/(b.*X))),0,intlim,'Arrayvalued',true)

I get the error message show below, while I'm expecting a number >0,<1

Warning: Infinite or Not-a-Number value encountered. 
> In funfun\private\integralCalc>iterateArrayValued at 267
  In funfun\private\integralCalc>vadapt at 130
  In funfun\private\integralCalc at 75
  In integral at 88

I'm also attempting a similar integration in the following form, but also not getting expected answers

pmax =  y

pmin = 0

ymax = 1    

ymin = @(x) x

xmax = 1

xmin = 0

integral3(@(x,y,p) (exp(-(integral(@(s)myfun(s,p),0,lam,'ArrayValued',true)./(k.*T)))),xmin,xmax,ymin,ymax,pmin,pmax,'Method','iterated')

Warning: Infinite or Not-a-Number value encountered. 
> In funfun\private\integralCalc>iterateScalarValued at 349
  In funfun\private\integralCalc>vadapt at 132
  In funfun\private\integralCalc at 75
  In funfun\private\integral2Calc>@(xi,y1i,y2i)integralCalc(@(y)fun(xi*ones(size(y)),y),y1i,y2i,opstruct.integralOptions) at 17
  In funfun\private\integral2Calc>@(x)arrayfun(@(xi,y1i,y2i)integralCalc(@(y)fun(xi*ones(size(y)),y),y1i,y2i,opstruct.integralOptions),x,ymin(x),ymax(x)) at 17
  In funfun\private\integralCalc>iterateScalarValued at 314
  In funfun\private\integralCalc>vadapt at 132
  In funfun\private\integralCalc at 75
  In funfun\private\integral2Calc>integral2i at 20
  In funfun\private\integral2Calc at 7
  In integral3>innerintegral at 137
  In funfun\private\integralCalc>iterateScalarValued at 314
  In funfun\private\integralCalc>vadapt at 132
  In funfun\private\integralCalc at 75
  In integral3 at 121 
Warning: The integration was unsuccessful. 
> In integral3 at 125

Thanks!

Answer 1

[Walter Roberson]

In your first case, if you let p = 0, then when t = 1, there is a singularity in mycircfunc at s = s_max .