Integration of Rational functions: Example2

Evaluate

displaymath98

Solution: First let us find the antiderivative

displaymath100

The main idea is first try to come up with the derivative of tex2html_wrap_inline102 in the top (or the numerator). Since tex2html_wrap_inline104 , we have

displaymath106

Hence

displaymath108

Since we have (see the table of Basic Formulas for Integrating Rational Functions)

displaymath110

displaymath112

and

displaymath114

we get

displaymath116

Therefore, we have

displaymath118

Easy calculations give

displaymath120

[Calculus] [Integration of Rational Functions] [More Examples]
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[Differential Equations] [Complex Variables] [Matrix Algebra]

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Author: Mohamed Amine Khamsi

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