Page 233 - Calculus Workbook For Dummies

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Chapter 11: Integration Rules for Calculus Connoisseurs

6. Solve the system of four equations from Steps 4 and 5. You get the following:
1 4
B = 0 C = - 1 D = - E =
3 3
If you find an easier way to solve for A through E, go to my Web site and send me an e-mail.
7. Integrate.
2
1
# x - x = # dx - # dx - # x - 4 dx
1
2
2
2
2
^ x + h x + 1 _i x + 2i 3 x + 1 x + 1 3 x + 2
1 _
1 1 2 2 2 x 2
= ln x + 1 - arctanx - ln x + i arctan + C
2 +
_
3 6 3 2
2
1 ^ x + 1h 2 2 x 2
= ln - arctanx + arctan + C
2
6 x + 2 3 2