Question: Calculus of variation with integral of control variable solving

Dear experts,

I am sorry to bother you again with different questions. I am attempting to get a solution with various methods so that I can grasp my problem as clear as possible. 

I am attempting maximizing this problem, so I am looking for functional solution of c(t). However, as you can see, in the optimization problem there is one bothering expression, which is a integral of c(h) from 0 to t. 

I looved optimal control theory book, but still I could not find a protocol example. 


int([int(e^(-rh)*[log(c(h)) + w - p*c(h)], h = 0 .. t)]*b*[int(c(h), h = 0 .. t)]*e^(-b*int(c(h), h = 0 .. t)), t = 0 .. infinity) 


How shall I approach this problem with Euler Lagrange in Maple? Thank you


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