Question

Calculus 2. Hi how do you decide whether to use substitution or integration by parts when looking at a integration problem.

Answer 1

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Answer 2

Ugh, I was in the process of writing a long comment, but the page suddenly refreshed on me -_-

Here were the highlights: Knowing which method to use is a matter of practice and an exercise in pattern recognition. Substitution allows you to rewrite an integrand as the derivative of a composition (so integration by substitution can be viewed as the opposite of the chain rule for differentiation). Integrating by parts allows you to work with an integrand that is a product of some function with the derivative of another (so integration by parts is the opposite of the product rule for differentiation).