I would like to solve the following equation:

 $$\bar{t} = \int_0^{\infty} t F(t) \, dt = \int_0^{\infty} e^{ -4 ms \int_0^t p(t') \, dt' } \, dt$$

Just focusing on the exponential section:

$ p(t')dt' $

and changing the notation slightly to substitute $t'$ with $u$.

I have worked out a few of the steps (see below) but I am not sure if the result has a closed form solution? The following are constants $m$, $s$, $N$.

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