James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

A98 Appendix I Answers to Odd-Numbered Exercises
33. x sec x 2 ln | sec x 1 tan x | 1 C 35. s3 2 1 3
22
37. 105 s2 2 8
105 39. ln | csc x 2 cot x | 1 C
41. 2 1 6 cos 3x 2 1 26 cos 13x 1 C 43. 1 15
45. 1 2 s2 47. 1 2 sin 2x 1 C
49. x tan x 2 ln | sec x | 2 1 2 x 2 1 C
51. 1 4 x 2 2 1 4 sinsx 2 d cossx 2 d 1 C
53. 1 6 sin 3x 2 1 18 sin 9x 1 C ƒ
_π
F
f
π
_π
ms80660-1
1
6et 7.2.51
8.13.06
F
_2 2
55. 0 57. 1 2 2 4 3 59. 0 61. 2 y4
63. (2s2 2 5 2) 65. s − s1 2 cos 3 tdys3d
Exercises 7.3 • page 491
1
1 C 3. sx 2 2 4 2 2 sec 21S x 2D 1 C
1. 2 s4 2 x 2
4x
1 sx 2 2 1d 3y2
1
5.
1 C 7.
3 x 3 s2 a 2
9. 2 3 s3 2 3 4 s2 11. 1 12
1
13. 6 sec21 sxy3d 2 sx 2 2 9ys2x 2 d 1 C
1
15. 16 a4 17. sx 2 2 7 1 C
19. ln | (s1 1 x 2 2 1)yx | 1 s1 1 x 2 1 C 21.
23. ln | sx 2 1 2x 1 5 1 x 1 1 | 1 C
25. 4 sin 21S x 2 1
2
D 1 1 4 sx 2 1d3 s3 1 2x 2 x 2
9
500
2 2 3 s3 1 2x 2 x 2 d 3y2 1 C
27. 1 2 sx 1 1dsx 2 1 2x 2 1 2 ln | x 1 1 1 sx 2 1 2x | 1 C
29. 1 4 sin21 sx 2 d 1 1 4 x 2 s1 2 x 4 1 C
33. 1 6 ss48 2 sec 21 7d 37. 3 8 2 1 3 4
41. 2 2 Rr 2 43. rsR 2 2 r 2 1 r 2 y2 2 R 2 arcsinsryRd
Exercises 7.4 • page 501
A
1. (a)
1 1 2x 1 B (b) A 3 2 x x 1 B x 1 C 2 x 1 3
3. (a) A x 1 B x 1 Cx 1 D
2 1 1 x (b) 1 1 A 2 x 1 B
x 2 1 1
5. (a) x 4 1 4x 2 1 16 1 A
x 1 2 1 B
x 2 2
Ax 1 B
(b)
x 2 2 x 1 1 1 Cx 1 D
x 2 1 2 1 Ex 1 F
sx 2 1 2d 2
7. 1 4 x 4 1 1 3 x 3 1 1 2 x 2 1 x 1 ln | x 2 1 | 1 C
D
1 1 x
π
C
x 2 2
9. 1 2 ln | 2x 1 1| 1 2 ln | x 2 1| 1 C 11. 2 ln 3 2
13. a ln | x 2 b | 1 C 15. 5 2 2 ln 2 2 ln 3 (or 5 2 2 ln 6)
17. 27 5 ln 2 2 9 5 ln 3 (or 9 5 ln 8 3)
19. 1 2 2 5 ln 2 1 3 ln 3 (or 1 2
21.
1 ln
27
32 )
1
4Fln | t 1 1 | 2 1
t 1 1 2 ln | t 2 1 | 2 1 1 C
t 2 1G
23. ln | x 2 1 | 2 1 2 lnsx 2 1 9d 2 1 3 tan21 sxy3d 1 C
25. 22 ln | x 1 1 | 1 lnsx 2 1 1d 1 2 tan 21 x 1 C
27. 1 2 lnsx 2 1 1d 1 tan 21 x 2 1 2 tan21S x 2D 1 C
29. 1 2 lnsx 2 1 2x 1 5d 1 3 2 tan21S x 1 1
2
D 1 C
31. 1 3 ln | x 2 1 | 2 1 6 lnsx 2 1 x 1 1d 2 1 s3
33. 1 4 ln 8 3
35. 2 ln | x | 1 3 2 lnsx 2 1 1d 1 1 2 tan21 x 1
37. 7 8 s2 tan 21S x 2 2
s2
D 1
tan21
2x 1 1
s3
x
2sx 2 1 1d 1 C
3x 2 8
4sx 2 2 4x 1 6d 1 C
39. 2 tan 21 sx 2 1 1 C
41. 22 ln sx 2 2 1 2 lnssx 1 1d 1 C
sx
3
43. 10 sx 2 1 1d 5y3 2 3 4 sx 2 1 1d 2y3 1 C
45. 2sx 1 3s 3 x 1 6s 6 x 1 6 ln | s 6 x 2 1 | 1 C
47. ln F se x 1 2d 2
se x 1 1dG1C
49. ln | tan t 1 1 | 2 ln | tan t 1 2 | 1 C
51. x 2 lnse x 1 1d 1 C
1 C
53. (x 2 1 2x 2 1
2) lnsx 2 2 x 1 2d 2 2x 1 s7 tan
21S D 1 C
s7
55. 2 1 2 ln 3 < 20.55
Z 1 C
57. 1 2 Z ln x 2 2
x
Z 1 C 61. 1 5 Z ln 2 tansxy2d 2 1
tansxy2d 1 2
63. 4 ln 2 3 1 2 65. 21 1 11 3 ln 2
67. t − ln 10,000 1 11 ln P 2 9000
P
1000
69. (a) 24,110 1
4879 5x 1 2 2 668 1
323 2x 1 1 2 9438
80,155
(b)
1
1
260,015
1
3x 2 7
22,098x 1 48,935
x 2 1 x 1 5
4822
4879 ln | 5x 1 2 | 2 334
323 ln | 2x 1 1 |
2 3146
80,155 ln | 3x 2 7 |
1 11,049
260,015 lnsx 2 1 x 1 5d 1 75,772 2x 1 1
tan21 1 C
260,015s19 s19
The CAS omits the absolute value signs and the constant of
integration.
1
75.
a n sx 2 ad 2 1
a n x 2 1
a n21 x 2 ∙ ∙ ∙ 2 1
2 ax n
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