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1.1 Rational functions

In applications, it is often useful to calculate indefinite integrals of rational functions such as

\int{\frac{x^{6}+12x^{2}+39x-44}{x^{3}+x^{2}+3x-5}}\,dx.

Recall that a typical rational function has the shape

h(x)={\frac{f(x)}{g(x)}}

where $f(x)$ and $g(x)$ are polynomials.

At the beginning of this section we will study a general method for integrating rational functions.