Integration by Parts/Proof Technique

Integration by Parts: Proof Technique
The technique of solving an integral in the form $\displaystyle \int \map f t \map G t \rd t$ in this manner is called integration by parts.

Its validity as a solution technique stems from the fact that it may be possible to choose $f$ and $G$ such that $G$ is easier to differentiate than to integrate.

Thus the plan is to reduce the integral to one such that $\displaystyle \int \map F t \map g t \rd t$ is easier to solve than $\displaystyle \int \map f t \map G t \rd t$.

It may be, of course, that one or more further applications of this technique are needed before the solution can be extracted.