Matemáticas aplicadas

62. x(x 2 a 2 ) 3/2 dx 1 5 (x2 a 2 ) 5/2
(x 2 a 2 ) 3/2
x
x 2 a 2
x
63. dx 1 3 (x2 a 2 ) 3/2 a 2 dx
1
3
64. x n (x 2 a 2 ) 3/2 dx x n1 (x 2 a 2 ) 3/2 n 1
n
x n2 x 2 a 2 dx
1
1
65. x n x 2 a 2 dx x n1 ((x 2 a 2 ) 3/2 a2 (n 1)
n
x n2 x 2 a 2 dx
2
n 2
(n 1)
(n 2)
Integrales que contienen ax 2 bx c
1
66. ax2 bx c
1
b2 4ac
2ax b b 2 4ac
2ax b b 2 4ac
dx ln (b 2 4ac 0)
Integrales que contienen exponenciales y logaritmos
67. e ax dx 1 a eax
1
68. a x dx a x
ln a
1
69. xe ax dx (ax 1)e ax
a
2
70. x n e ax dx 1 a xn e ax n a xn1 e ax dx
1 1
71. dx [ax ln (b ce ax )] (ab 0)
b ce ax a b
72. ln ⏐x⏐dx x ln⏐x⏐ x
73. x ln ⏐x⏐ dx 1 2 x2 ln⏐x⏐ 1 4 x2
1
74. x n ln ⏐x⏐ dx x n1
n 1 ln ⏐x⏐ 1
n 1
(n 1)
ln⏐x⏐
75. dx ln⏐ln⏐x⏐⏐
x
76. ln n ⏐x⏐ dx x ln n ⏐x⏐ x ln n1 ⏐x⏐ dx
77. x m ln n ⏐x⏐ dx m
1
ln
78. n ⏐x⏐ 1
dx ln n1 ⏐x⏐
x n 1
x m1 ln n ⏐x⏐ n x m ln n1 ⏐x⏐ dx (m 1)
1
778 APÉNDICE II TABLA DE INTEGRALES