Uploaded by vchaynikov

worksheet on partial fractions (helpful for integration)

advertisement
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 coe´Čâcients (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
Download