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