Original
With some experience, it is (usually) not too hard to see what to
substitute as {{MATH_65}}. We will work through the following examples in the
same way that we did for Example {{CMD_66}}.
{{CMD_67}}
Compute:
{{MATH_68}}
{{CMD_69}}
Here we set {{MATH_70}}, so {{MATH_71}}. Then
it follows that {{MATH_72}}. Therefore
{{ENV_73}}
Notice that this example is an indefinite integral and not a definite
integral, meaning that there are no limits of integration. So we do
not need to worry about changing the endpoints of the integral. However,
we do need to back-substitute into our answer, so that our final
answer is a function of {{MATH_74}}. Recalling that {{MATH_75}}, we have
our final answer
{{MATH_76}}
Reminder: you can always verify your result by differentiating.