Integrate in R is failing when upper limit is Inf

I need to numerically approximate the variance of the logarithm of the sum of two log-normal random variables. I'd like to do this in R, here's an example:

################
## Setup data ##
################

sdX1 = 0.33
sdX2 = 0.70
muX1 = log(32765) - 0.5 * sdX1^2
muX2 = log(52650) - 0.5 * sdX2^2

####################################
## PDF for sum of 2 lognormal RVs ##
####################################

d2lnorm = function(z, muX1, muX2, sdX1, sdX2){

    #PDFs
    L1 = distr::Lnorm(meanlog = muX1, sdlog = sdX1)
    L2 = distr::Lnorm(meanlog = muX2, sdlog = sdX2)

    #Convlution integral
    L1plusL2 = distr::convpow(L1 + L2, 1)

    #Density function
    f.Z = distr::d(L1plusL2)

    #Evaluate
    return(f.Z(z))

}

############################################
## Expectation for sum of 2 lognormal RVs ##
############################################    

ex2lnorm = function(muX1, muX2, sdX1, sdX2){    

    #E(g(x)) = integral of g(x) * f(x) w.r.t x
    integrate(function(z) log(z) * d2lnorm(z, muX1 = muX1, muX2 = muX2, sdX1 = sdX1, sdX2 = sdX2), lower = 0, upper = +Inf)$value

}

##############
## Run code ##
##############

ex2lnorm(muX1, muX2, sdX1, sdX2)

However, the integral evaluates to 0. If I change the upper limit of integrate to a large number it works. However, I'm running a bunch of simulations and I can't fiddle with the upper limit to get it to work every time. Is there some other way to get this to work consistently?

What you could do if finding the maximum upper value that doesn't give 0:

ex2lnorm = function(muX1, muX2, sdX1, sdX2){    

  f <- function(z) log(z) * d2lnorm(z, muX1 = muX1, muX2 = muX2, sdX1 = sdX1, sdX2 = sdX2)

  upper <- 2^10
  cond.lower <- FALSE
  repeat {
    new <- integrate(f, lower = 0, upper = upper)$value
    if (new > 0) cond.lower <- TRUE
    if (cond.lower && new == 0) break
    upper <- upper * 2
    prev <- new
  }

  prev
}