Original
If substitution works to calculate an integral (and that is not always the
case!), a common trick to find what to substitute for is to locate the
``ugly'' part of the function being integrated. We then substitute
for the ``inside'' of this ugly part. While this technique is
certainly not rigorous, it can prove to be very helpful. This is
especially true for students new to the technique of substitution.
The next two problems are really good examples of this philosophy.