Worksheet on Partial Fractions and Integration 1. Write out the appropriate form of partial fraction decomposition (use unknowns A, B, C ...). 3x (0) 2 = x + 2x + 2 (1) (2) x2 3x = + 3x + 2 x2 3x = + 2x + 1 (3) x3 = x2 + 4 (4) 1 = x3 + 1 2. Find the unknown coeﬃcients (A, B, C ...) (a) for problem 1(0). (b) for problem 1(1). (c) for problem 1(2). 3. Use ∫ your results above to integrate: 3x (a) dx x2 + 2x + 2 ∫ (1) x2 3x dx + 3x + 2 x2 3x dx + 2x + 1 ∫ (2) ∫ 4. Solve: dx 4 − x2 1 1 1 2−x Answer: − ln |2 − x| + ln |2 + x| + C or ln | |+C 4 4 4 2+x Questions: 1. Where did ’−’ come from in the answer? ∫ 2. if you had dx dx what would be your antiderivative and why? 4 − 5x