I seem to have seen quite a lot of integrals in the form:
$$\int_0^\infty \frac{\text{d}x}{e^x+(1+x^n)}$$
But none of those hold a closed forms (at least to my knowledge)
$$\Large\color\red{\int_0^\infty \frac{\text{d}x}{e^x+x^n}}$$
Does a closed form exist of this integral? (in terms of $n$)