Math 2300 Section 005 – Calculus II – Fall 2010
Substitution Examples – August 23–24, 2010
Guess and Check & Mechanical Substitution Examples

Solution: If you guess that is an appropriate antiderivative, then you differentiate to via the chain rule. But, we're now off by a scalar factor, which is an easy fix. Just multiply your antiderivative by half. We end up with
and we know this is the answer because we can differentiate to .