How to calculate the integral of log-normal distribution with MATLAB - matlab

Question

I want to calculate the part-expectation of log-normal distribution via:
m = 1;
v = 2;
mu = log((m^2)/sqrt(v+m^2));
sigma = sqrt(log(v/(m^2)+1));
syms x;
d = x*lognpdf(x,mu,sigma);
int(d, x, 0, 10);
However, MATLAB says:
Error using symfun>validateArgNames (line 211) Second input must be a
scalar or vector of unique symbolic variables.
Error in symfun (line 45)
y.vars = validateArgNames(inputs);
Error in sym/subsasgn (line 771)
C = symfun(B,[inds{:}]);
Error in lognpdf (line 36) x(x <= 0) = Inf;
Error in untitled (line 7) d = x*lognpdf(x,mu,sigma);
I even tried to just calculate the integral of the pdf by:
m = 1;
v = 2;
mu = log((m^2)/sqrt(v+m^2));
sigma = sqrt(log(v/(m^2)+1));
syms x;
d = lognpdf(x,mu,sigma);
int(d, x, 0, 10);
But there are still errors, and MATLAB says:
Error using symfun>validateArgNames (line 211) Second input must be a
scalar or vector of unique symbolic variables.
Error in symfun (line 45)
y.vars = validateArgNames(inputs);
Error in sym/subsasgn (line 771)
C = symfun(B,[inds{:}]);
Error in lognpdf (line 36) x(x <= 0) = Inf;
Error in untitled (line 7) d = lognpdf(x,mu,sigma);
I really don't know what happened. Should the integral of the pdf be the cdf?

Answer 1

Similar to an answer several months ago, the Statistics Toolbox doesn't support the Symbolic Toolbox currently.
Therefore, you can proceed by hard coding the PDF itself and integrating it:
d = exp(-(log(x)-mu)^2/(2*sigma^2))/(x*sigma*sqrt(2*pi));
int(d, x, 0, 10);
Or you can use the logncdf function, which may be cleaner.