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7.4 Partial Fractions. We integration!. Tips for Integration. Try anti-differentiation first Try u-substitution Check for Inverse trig forms If there is an extra variable in the denominator, try completing the square Integration by Parts Check for the common forms - PowerPoint PPT Presentation
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We integration!
7.4 PARTIAL FRACTIONS
Tips for Integration1. Try anti-differentiation first2. Try u-substitution3. Check for Inverse trig forms
o If there is an extra variable in the denominator, try completing the square
4. Integration by Partso Check for the common forms
5. Integration by Partial Fractionso Try 1 of the 3 cases
Use Algebra!Don’t be afraid to mix multiple techniques in
1 problem!
3 Cases for Partial FractionsCase I – The denominator has distinct
factors
Case II – The denominator has repeating factors
Case III – The denominator has a quadratic that won’t factor
If the degree in the numerator is higher than the degree in the denominator, use long division first.
Case I – The denominator has distinct factors
2
9
3 10
xdx
x x
Case II – The denominator has repeating factors
2
4
1 1
xdx
x x
Case III – The denominator has a quadratic that won’t factor
2
3
2 4
4
x xdx
x x
