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How do you compute something like

The integral on the right is then easy to do (the answer involves 's).

But *how on earth* do you right the rational function
on the left hand side as a sum of the nice terms
of the right hand side? Doing this is called
``partial fraction decomposition'', and it is
a fundamental idea in mathematics. It relies on
our ability to factor polynomials and saolve linear
equations. As a first hint, notice that

Before describing the secret behind (5.4.1), we'll discuss some background about how polynomials and rational functions work.

If is a polynomial, the roots of correspond to the factors of . Thus if

For example,

is a rational function.

For example, for (5.4.2) the poles are at , , and . They have multiplicity , , and , respectively.

William Stein 2006-03-15