Direct Integration for Multi-Leg Amplitudes: Tips, Tricks, and When They Fail

Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly multi-particle diagrams. We review variety of results by the authors in which this method, employed with some care, can compute diagrams up eight particles and four loops. also highlight situations method fails due an algebraic obstruction. In large number cases obstruction be associated Calabi-Yau manifold.