funk <- function(x,b) { 10^b * exp(-x/10) }

lambda <- function(y,k) { exp(-k*y) }

funk1 <- function(y,x,xb,b,k) {
funk(x-xb-y,b) *exp(- integrate(lambda, lower=0, upper = y, k=k)$value) }

funk2 <-function(x,xb,b,k) {
integrate(funk1, lower= 0, upper=x-xb, x=x,xb=xb, b=b,k=k)$value }

funk2_vc <- Vectorize(funk2)

optim_funk2 <- function(param,x,xb) {
b <-param[1]
k <- param[2]
R1 <- sum((y - funk2_vc(xx,xb,b,k))^2)
-log(R1) }

fit <- optim(par=c(5, 0.05), fn=optim_funk2)

xx <- seq(0,500,5)
xb <- seq(0,100,1)
y <- seq(1000,0,-10)