Integration by parts is one of the most time-consuming methods of integration that we learn in calculus, second only to the dreaded trig-substitution. However, in certain settings, we can speed up the process by using tools from linear algebra. By considering functions as vectors, we can find a basis for a subspace that allows us to compute integrals via a simple matrix multiplica-tion. Will this discovery lead to a paradigm shift in integration techniques? No! But it is an interesting intersection of ideas. Food and drinks will be provided!