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Lecture

# 7.4 Integration of Rational Functions by Partial Fractions Question #5 (Medium)

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Mathematics

MAT136H1

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Winter

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7.4 Integration Techniques
Partial Fractions for Rational Functions
Question #5 (Medium): Rationalizing Substitutions
Strategy
Non-rational functions refer to those containing root functions in either the numerator or denominator,
but also those that include trigonometric or exponential functions. Either way, a simple variable is used
to substitute as the building block to represent the function type. Then factor the denominator, split the
rational function, then take integral. Remember to re-substitute back in the original expression.
Sample Question
By substitution express the integral as a rational function and then evaluate the integral.
∫
Solution
First factor the function in the denominator, so that: ( )( ).
Notice the rational function is in the form of chain rule.

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