How to get geom_function to work with a two-step function?

I find it really hard to explain what I am trying to do with words, so I am just going to post my code below.

fun <- function(a, x) {
  output <- a*dlnorm(a, 2.72 - x, 0.52)
  return(output)
}
fun2 <- function(x) {
  output2 <- integrate(fun, lower = 0, upper = 200, x = x)
  return(output2)
}
a <- seq(-5, 5, .1)
list <- list()
for(ai in 1:length(a)){
  list[[ai]] <- fun2(a[[ai]])
}
list %>% 
  map(pluck, "value") %>% 
  unlist() %>% 
  bind_cols(a) %>% 
  ggplot(aes(x = `...2`, y = `...1`)) + 
  geom_line()

So we first have one function which takes on arguments of a and x. Then we make another function that integrates the first one over the values of x and finally we plot the integral over the values of a.

Notice that I am computing the curve for the plot manually by using a for loop. I would like to avoid using the for loop and I would like to directly do this via geom_function. However, I don't know how to approach this. I've been trying this:

ggplot() + 
  geom_function(fun = fun2) + 
  xlim(-5, 5)

But unfortunately that doesn't work. So what is the proper way to specify this in the code?

The integrate function doesn't return a vector from your vector input. It expects just a single input, and returns a structure as output, e.g.

> str(fun2(1))
List of 5
 $ value       : num 6.39
 $ abs.error   : num 9.92e-06
 $ subdivisions: int 6
 $ message     : chr "OK"
 $ call        : language integrate(f = fun, lower = 0, upper = 200, x = x)
 - attr(*, "class")= chr "integrate"

So what you need to do is make fun2 return a vector of values of the same shape as x. That involves a loop, but you can hide that by using the Vectorize function. For example,

fun2 <- function(x) {
  # This definition only handles a scalar x
  integrate(fun, lower = 0, upper = 200, x = x)$value
}
# This makes it handle a vector x by looping over the values
fun2 <- Vectorize(fun2)

Now geom_function(fun = fun2) will be fine with it.