Integration by parts is for functions that can be written as the product of another function and a third function's derivative. A good rule of thumb to follow would be to try u-substitution first, and then if you cannot reformulate your function into the correct form, try integration by parts.

Why do we use integration?

The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus, and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others.

When can we integrate a function?

Explanations (1) Since the integral is defined by taking the area under the curve, an integral can be taken of any continuous function, because the area can be found. However, it is not always possible to find the indefinite integral of a function by basic integration techniques.