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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.,
.
∫
++
+
dX
XXX
X
34
5
2
5
∫∫
∞→
∞
=
ε
ε
1
2
1
2
lim
x
dx
x
dx