The Chain Rule is a way of differentiating two (or more) functions
In many simple cases the above formula/substitution is not needed
The same can apply for the reverse – integration
Integrating with reverse chain rule
In more awkward cases it can help to write the numbers in before integrating
STEP 1: Spot the ‘main’ function
STEP 2: ‘Adjust’ and ‘compensate’ any numbers/constants required in the integral
STEP 3: Integrate and simplify
If in doubt you can always use a substitution.
Differentiation is easier than integration so if stuck try the opposite, eg. sin and cos are linked (remember that minus!) so if integrating a sin function, start by differentiating the corresponding cos function.
Lastly, check your final answer by differentiating it.