If you just want the value of an integral, maybe not. If you want to understand the integral, or manipulate it in different ways, yeah there's value. Frequently

If you just want the value of an integral, maybe not. If you want to understand the integral, or manipulate it in different ways, yeah there's value. Frequently, a computational solver will spit out some giant expression, while if you did it manually, you'd end up with something more compact, perhaps making new intuitive definitions along the way (generally manual common subexpression elimination and factoring).