One venerable technique in the solution of differential equations is
the `method of undetermined coefficients'. You ** guess** the form
of the answer, with some unknown coefficients, and then use the problem
under discussion to discover the coefficients. For integration, the
technique might go something like this:

is to be found. We * guess* that the answer is of the form

and differentiate both the integral and our guess to get the following:

and we set all the coefficients to zero, which gives us a (triangular) linear system for the unknown coefficients. This gives us

so our answer is

which is correct.

This can be done more efficiently for some problems. See the worksheet
`undet.ms`

for the next section.

Thu Nov 23 10:59:42 PST 1995