Does anyone know how to simplify the actually hard part of calculus: solving integrals? I refer to the million different substitutions and trig/hyperbolic formulas, along with the endless amount of other heuristics. I wonder if there's a way to bypass or simplify most of that.
It's not really possible. It's akin to saying simplify multiplying large numbers or long division. It can be sometimes done by having a heap of tricks up your sleeve, by practicing a bunch you might get better at guessing which trick to use when. The usefulness of knowing these tricks and recognising when to use them is entirely dependent on your motivations.