If a symbolic solution cannot be found for the inner integral, you can use the matlab function ‘integral2’ for your task. If you read the instructions for it at:
https://www.mathworks.com/help/matlab/ref/integral2.html,
you will see that it allows the inner integral limits to be functions of the outer variable rather than fixed numerical values - in your case the lower inner limit is s itself. Hence, even though your integrand is a function only of s’, it should still arrive at a solution for the double integral.
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