1. Miss Battaglia AP Calculus
8-5 Partial Fractions
Miss Battaglia
AP Calculus

2. Case 1: Denominator contains only linear factors
Factor the denominator
Break up the fraction on the right into a sum of fractions, where each factor of the denominator in Step 1 becomes the denominator of a separate fraction. Then put unknowns in the numerator of each fraction.
Multiply both sides of this equation by the denominator of the left side.
Take the roots of the linear factors and plug them –one at a time-into x in the equation from Step 3, and solve for unknowns.
Plug these results into the A and B in the equation from Step 2.
Split up the original integral into the partial fractions from Step 5 and you’re home free!

3. Case 2: The denominator contains irreducible quadratic factors
Factor the denominator
Break up the fraction into a sum of “partial fractions”
Multiply both sides of this equation by the left-side denominator.
Take the roots of the linear factors and plug them- one at a time- into x in the equation from Step 3, and then solve.
Plug into Step 3 equation the known values of A and B and any two values for x not used in Step 4 to get a system of two equations in C and D.
Solve the system of equations.
Split up the original integral and integrate.

4. Distinct Linear Functions
Write the partial fraction decomposition for

5. Example
Write the partial fraction decomposition for

6. Example
Write the partial fraction decomposition for

7. Classwork/Homework
Read 8.5 Page 561 #7-15