One of my favorite bits of my PhD dissertation was factoring an intractable 3-dimensional integral

\iiint f(x, y, z) dx dy dz = \int [\int g(x, y) dx]*[\int h(y, z) dz] dy

which greatly accelerated numerical integration (O(n^2) rather than O(n^3)).

My advisor was not particularly impressed and objectively I could have skipped it and let the simulations take a bit longer (quite a bit longer--this integration was done millions of times for different function parameters in an inner loop). But it was clever and all mine and I was proud of it.