This integral is giving me a headache:
$$\int_{-b}^{b}\frac{xf'(x)}{f(x)}dx$$
where $f(x)=(c + d - e)\text{sech}(ab)\cosh(a x)+(c-d)\text{csch}(ab)\sinh(a x) + e$
I could not come up with any general or $f$-specific way of approximating it. While Euler’s did not simplify much, a clever use of Taylor expansion might help. By approximation, I mean a general approximated form of solution (without having specific values). Any effort is greatly appreciated?