Evaluate the integral using substitution with the power rule
When solving an integral that requires the power rule and substitution, the first step is to identify a part of the expression that would be simpler if rewritten in terms of a new variable. In this case, you look for a piece of the function that can be replaced with a new variable to make the integral easier to manage. This is where substitution comes in.
Once you've chosen your substitution, you change the variable in the integral to match your new substitution. This transforms the original problem into one that uses simpler terms. Often, after substitution, the integral will involve a basic power of the new variable, which is when you can apply the power rule. The power rule is a fundamental rule that makes it easier to find the antiderivative when the function involves powers of the variable.
After applying the power rule to the simplified expression, the last step is to undo the substitution by replacing the new variable back with the original one. This ensures that your final answer is in terms of the original variable, completing the process of integration.