Integration of softplus function

The softplus function $f(x)=\ln(1+e^x)$ is a good approximation for $\max\{x,0\}$.However, finding the primitive of $f(x)=\ln(1+e^x)$ seems to be quite difficult. Is there any tractable way to do that? For example, we need to compute$$ \int_{a}^{b}\ln(1+e^x) d x $$