Integration By Partial Fractions; Improper Integrals - HP 50g User Manual

Integration by partial fractions

Function PARTFRAC, presented in Chapter 5, provides the decomposition of a
fraction into partial fractions. This technique is useful to reduce a complicated
fraction into a sum of simple fractions that can then be integrated term by term.
For example, to integrate
we can decompose the fraction into its partial component fractions, as follows:
The direct integration produces the same result, with some switching of the terms
(Rigorous mode set in the CAS – see Chapter 2):

Improper integrals

These are integrals with infinite limits of integration. Typically, an improper
integral is dealt with by first calculating the integral as a limit to infinity, e.g.,
5
5
X
∫
4 3
2
X X
dx
∫ ∫
lim
2
1
x
dX
X
dx
.
2
1
x
Page 13-20