7.4 Integration of Rational Functions by Partial Fractions Question #4 (Medium)
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7.4 Integration Techniques
Partial Fractions for Rational Functions
Question #4 (Medium): Rationalizing Substitutions
Non-rational functions are rationalized through substitution. Assign root function to a variable, then
convert non-rational function into rational function. Then rest is same as working with rational functions.
Remember to substitute back in the original root expression at the end.
Apply substitution to express the integral as a rational function, then evaluate the integral.
, then so that and
and , then
Using the long division, the quotient is and remainder , thus:
Substitute back in
Therefore, the integral is evaluated as:
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