# 9.3  Integration of Rational Functions by Partial Fractions
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 9.3.
# In-line plots have been removed to conserve disk space.
> restart; f:=(x^2 - 3*x + 1) / (x^3 + x^2 - 2*x);

                                2
                               x  - 3 x + 1
                          f := -------------
                                3    2
                               x  + x  - 2 x

> fpar:=convert(f, parfrac, x);

                                         1           1
              fpar := - 1/2 1/x + 11/6 ----- - 1/3 -----
                                       x + 2       x - 1

> Int(fpar, x); value(");

                /
               |                     1           1
               |  - 1/2 1/x + 11/6 ----- - 1/3 ----- dx
               |                   x + 2       x - 1
              /


             - 1/2 ln(x) + 11/6 ln(x + 2) - 1/3 ln(x - 1)

>