8-5 Partial Fractions. Miss Battaglia AP Calculus. Case 1: Denominator contains only linear factors. Factor the denominator
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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!