Solutions to exercises 637
Section 6.5
Section 6.6
68.tan
− 1
(x 1 + 1 2) 1 + 1 C
73.ln
tan
tan
12
12
−
θ
θ
C
−
++
++
−
1
2
514
45
52
2
1
x
xx
tan (xC)
1
2
452 2
21
ln(xx++−) tan (x C++)
−
1
2
2
2
45
1
2
tan ( )
−
++
++
x +
x
xx
C
1
2
3
4
2
2
ln
x
x
C
1
2
45
2
ln(xx C+++)
++
21 xC3 ln( )+
1
2
71262ln( )xx+− + ln( )
ln
()
()
x
x
C
4
3
2
1
7
21
3
ln
x
x
C
−
1
2
T
12
3
/
kT
m
12
8
/
kT
πm
1
8
1
8
π
2
1
4
1
60
−+
8
315
cosx
C
−−
sin cos sin cos
42
105
4
315
xx xx
sin cos sin cos
63 6
921
xx xx
−
−n
n
xdx
n1
2Zsin
Zsin sin cos
nnxdx
n
=− xx
−
1
11
13
() 23 −
−
e
πe
ab
abxbbxC
ax()
(cos sin )
22
++
−+ +
−
1
5
(sin22 2xxeCcos )
x75.ln 1 (1 1 + 1 tan 1 θ 2 2) 1 + 1 C
Chapter 7
Section 7.2
1.u
r1 = 111 + 13 r; 1 u
r1 = 1 u
r− 11 + 1 3, u
0
1 = 11
2.u
r1 = 13
r; 1 u
r1 = 13 u
r− 1, u
0
1 = 11
1 , 3 , 5 , 11 , 21 , 43
10.u
n1 = 1 u
0
, all n 11. 0 12.∞
- 0 14. 1 15. 0
- 325 17. 2
Section 7.3
- (i)n(2n 1 − 1 1) (ii) 190
- (i) (ii)− 195
- (i) (ii) 29524
- (i)
(ii)
- 11 + 15 x 1 + 110 x
2
1 + 110 x
3
1 + 15 x
4
1 + 1 x
5
- 11 + 17 x 1 + 121 x
2
1 + 135 x
3
1 + 135 x
4
1 + 121 x
5
1
- 17 x
6
1 + 1 x
7
- 1 , 3 , 3 , 1 27. 1 , 4 , 6 , 4 , 1
- 1 , 7 , 21 , 35 , 21 , 7 , 1
x
x
x
n12
12
−
−
()
xxx
32 n2
1
1
()−
−
1
2
3
1
3
1 499975
9
−
≈.
3
2
1
1
3
−
n1
2
() 31
n−
n
n
2
()11 5−
1
1
2
1
2
5
2
13
2
29
2
, ,−,−,− ,−
1
1
2
1
6
1
24
1
120
1
720
,,, , ,
1
3
1
8
1
15
1
24
1
35
1
48
,, , , ,
1
2
3
4
9
8
27
16
81
32
243
,,, , ,
0
1
2
1
3
2
2
5
2
,,, ,,
uu
u
u
rrrr=−
=− =
−
1
55
1
1
0
; ,
1
2
22
1
tan ( tan )
−
θ +C