Page 706 - Handbook Of Integral Equations

2
dx 1 1 x
59. = + .

2
2
2 2
2
2
2
x(a – x ) 2a (a – x ) 2a 4 ln a – x 2
dx 1 1 1 x
2
60. = + + .

4
2 2
2
2
2
2
2
2 3
2
x(a – x ) 4a (a – x ) 2a (a – x ) 2a 6 ln a – x 2
3
3
Integrals containing a + x .
dx 1 (a + x) 1 2x – a
2
61. = ln + √ arctan √ .
3
2
a + x 3 6a 2 a – ax + x 2 a 2 3 a 3
dx x 2 dx

62. = + .
3 2
3
3
3
3
3
(a + x ) 3a (a + x ) 3a 3 a + x 3
xdx 1 a – ax + x 1 2x – a
2 2
63. = ln + √ arctan √ .
3
a + x 3 6a (a + x) 2 a 3 a 3
xdx x 1 xdx
2
64. = + .
3
3
3
3 2
3
3
(a + x ) 3a (a + x ) 3a 3 a + x 3
x dx 1 3 3
2
65. = ln |a + x |.
3
a + x 3 3
dx 1 x
3
66. = .

3
3
3
x(a + x ) 3a 3 ln a + x 3
dx 1 1 x
3
67. = + .

3
3 2
3
3
3
3
x(a + x ) 3a (a + x ) 3a 6 ln a + x 3

dx 1 1 xdx
68. = – – .
3
2
3
3
3
x (a + x ) a x a 3 a + x 3
dx 1 x 4 xdx
2
69. = – – – .
3
3
2
3 2
6
3
3
6
x (a + x ) a x 3a (a + x ) 3a 6 a + x 3
3
3
Integrals containing a – x .
dx 1 a + ax + x 1 2x + a
2 2
70. = ln + √ arctan √ .
3
a – x 3 6a 2 (a – x) 2 a 2 3 a 3
dx x 2 dx

71. = + .
3
3
3
3 2
3
3
(a – x ) 3a (a – x ) 3a 3 a – x 3
xdx 1 a + ax + x 1 2x + a
2 2
72. = ln – √ arctan √ .
3
a – x 3 6a (a – x) 2 a 3 a 3
xdx x 1 xdx
2
73. = + .
3
3 2
3
3
3
3
(a – x ) 3a (a – x ) 3a 3 a – x 3
x dx 1 3 3
2
74. = – ln |a – x |.
3
a – x 3 3
dx 1 x
3
75. = .

3
3
3
x(a – x ) 3a 3 ln a – x 3
dx 1 1 x
3
76. = + .

3 2
3
3
3
3
3
x(a – x ) 3a (a – x ) 3a 6 ln a – x 3

dx 1 1 xdx
77. = – + .
3
2
3
3
3
x (a – x ) a x a 3 a – x 3
dx 1 x 4 xdx
2
78. = – – + .
3
3
3 2
6
6
3
2
3
x (a – x ) a x 3a (a – x ) 3a 6 a – x 3
© 1998 by CRC Press LLC
© 1998 by CRC Press LLC
Page 690