I'm stuck on an integral
$$\int \tan \left( a_0 \, e^{(-x/L)} \right) \,dx $$
where $a_0$ is a constant.
I've tried doing a substitution with $ u = a_0e^{x/L}$ but it gave me
$$\int \frac{\tan(u)}{u}du $$ which Wolfram Alpha didn't like.
Any help would be appreciated.
Just like other trigonometric integrals, it does not possess a closed form expression. See also inverse tangent integral. This can be proven using either Liouville's theorem or the Risch algorithm. Alternately, expand $\tan(x)$ into its well-known Taylor series, then reverse the order of summation and integration.