In some instances, we must evaluate a collection of nested functions. Similar to the technique used in the differential Chain Rule, the approach for evaluating an indefinite integral starts by identifying which functions are the 'container' functions and which are the 'nested' functions.
Once we identify which functions are nested within other functions, we replace one of the functions with a different variable symbol. This is done to make the integration process easier as it becomes simpler to manipulate the expression using the conventional rules of integration.
Finally, we re-substitute the original variable symbols as the evaluation is completed. Here we evaluate: $\int {\left(3x+2\right)}^{4}dx$
Substituting Variables