Integral of exponential function that contains another integral

Hello everyone,

I have the following integral:

where and c is a constant in one case and in another case. In addition, my r values are

r = linspace(0,4,100);

Can you please help me with the way to code this?

Thank you,

djr

Answer 1

[Ameer Hamza]

Try this

inner_int = @(t) integral(@(s) (1-exp(-s))./s, 0, t);
H = @(xi) integral(@(t) exp(-t+3*inner_int(t)), 0, xi, 'ArrayValued', 1);

r = linspace(0,4,100);
c = 1; % for example
Xi = c*r.^2;
H_val = zeros(size(Xi));
for i=1:numel(Xi)
    H_val(i) = H(Xi(i));
end
plot(Xi, H_val);
xlabel('\xi');
ylabel('H(\xi)')

[djr]

This is working perfectly. You helped me a lot!

[Ameer Hamza]

I am glad to be of help.