You're assuming that you want to express the integral as an elementary function, or as a member of another narrow class of functions. It's only in that case tha

You're assuming that you want to express the integral as an elementary function, or as a member of another narrow class of functions. It's only in that case that the lack of a chain rule is a problem. What you actually want is the ability to evaluate the integral to within epsilon numerically, which is a much more flexible problem. But then again, it's not clear what the OP meant by "automatic integration" anyway.