Unformatted text preview: x) are polynomials. An integral of a rational function
may be evaluated if the rational function is expressed as sums of simpler fractions (called partial fractions ) that we already
know how to integrate. Finding partial fraction decompositions are usually quite messy and students are prone to making
errors. This question illustrates how Maple can be used to determine a partial fraction decomposition of a rational function.
In this course, you are required to know how to ﬁnd partial fraction decompositions by hand. However, you can use Maple
to check your work on assignments!
For example, in Maple ﬁnd the partial fraction decomposition for
x2 + 2x − 1
x(2x − 1)(x + 2)
First you must tell Maple the expression for the integrand:
[> integrand := ( x∧2 + 2*x -1 ) / (x * (2*x-1) * (x+2) );
Next, enter Maple’s convert to partial fraction commmand as follows:
[> convert( integrand, parfrac, x);
Maple returns the partial fraction decomposition of integrand as:
2x 5(2x − 1) 10(x + 2)
At this point,...
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