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