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Chapter 3
Listing of integrals
3.1
\(\int x^3 (A+B x) \sqrt{a+b x^2} \, dx\)
3.2
\(\int x^2 (A+B x) \sqrt{a+b x^2} \, dx\)
3.3
\(\int x (A+B x) \sqrt{a+b x^2} \, dx\)
3.4
\(\int (A+B x) \sqrt{a+b x^2} \, dx\)
3.5
\(\int \frac{(A+B x) \sqrt{a+b x^2}}{x} \, dx\)
3.6
\(\int \frac{(A+B x) \sqrt{a+b x^2}}{x^2} \, dx\)
3.7
\(\int \frac{(A+B x) \sqrt{a+b x^2}}{x^3} \, dx\)
3.8
\(\int x^3 (A+B x) (a+b x^2)^{3/2} \, dx\)
3.9
\(\int x^2 (A+B x) (a+b x^2)^{3/2} \, dx\)
3.10
\(\int x (A+B x) (a+b x^2)^{3/2} \, dx\)
3.11
\(\int (A+B x) (a+b x^2)^{3/2} \, dx\)
3.12
\(\int \frac{(A+B x) (a+b x^2)^{3/2}}{x} \, dx\)
3.13
\(\int \frac{(A+B x) (a+b x^2)^{3/2}}{x^2} \, dx\)
3.14
\(\int \frac{(A+B x) (a+b x^2)^{3/2}}{x^3} \, dx\)
3.15
\(\int x^3 (A+B x) (a+b x^2)^{5/2} \, dx\)
3.16
\(\int x^2 (A+B x) (a+b x^2)^{5/2} \, dx\)
3.17
\(\int x (A+B x) (a+b x^2)^{5/2} \, dx\)
3.18
\(\int (A+B x) (a+b x^2)^{5/2} \, dx\)
3.19
\(\int \frac{(A+B x) (a+b x^2)^{5/2}}{x} \, dx\)
3.20
\(\int \frac{(A+B x) (a+b x^2)^{5/2}}{x^2} \, dx\)
3.21
\(\int \frac{(A+B x) (a+b x^2)^{5/2}}{x^3} \, dx\)
3.22
\(\int \frac{x^3 (A+B x)}{\sqrt{a+b x^2}} \, dx\)
3.23
\(\int \frac{x^2 (A+B x)}{\sqrt{a+b x^2}} \, dx\)
3.24
\(\int \frac{x (A+B x)}{\sqrt{a+b x^2}} \, dx\)
3.25
\(\int \frac{A+B x}{\sqrt{a+b x^2}} \, dx\)
3.26
\(\int \frac{A+B x}{x \sqrt{a+b x^2}} \, dx\)
3.27
\(\int \frac{A+B x}{x^2 \sqrt{a+b x^2}} \, dx\)
3.28
\(\int \frac{A+B x}{x^3 \sqrt{a+b x^2}} \, dx\)
3.29
\(\int \frac{x^3 (A+B x)}{(a+b x^2)^{3/2}} \, dx\)
3.30
\(\int \frac{x^2 (A+B x)}{(a+b x^2)^{3/2}} \, dx\)
3.31
\(\int \frac{x (A+B x)}{(a+b x^2)^{3/2}} \, dx\)
3.32
\(\int \frac{A+B x}{(a+b x^2)^{3/2}} \, dx\)
3.33
\(\int \frac{A+B x}{x (a+b x^2)^{3/2}} \, dx\)
3.34
\(\int \frac{A+B x}{x^2 (a+b x^2)^{3/2}} \, dx\)
3.35
\(\int \frac{A+B x}{x^3 (a+b x^2)^{3/2}} \, dx\)
3.36
\(\int \frac{x^3 (A+B x)}{(a+b x^2)^{5/2}} \, dx\)
3.37
\(\int \frac{x^2 (A+B x)}{(a+b x^2)^{5/2}} \, dx\)
3.38
\(\int \frac{x (A+B x)}{(a+b x^2)^{5/2}} \, dx\)
3.39
\(\int \frac{A+B x}{(a+b x^2)^{5/2}} \, dx\)
3.40
\(\int \frac{A+B x}{x (a+b x^2)^{5/2}} \, dx\)
3.41
\(\int \frac{A+B x}{x^2 (a+b x^2)^{5/2}} \, dx\)
3.42
\(\int \frac{A+B x}{x^3 (a+b x^2)^{5/2}} \, dx\)
3.43
\(\int \frac{(1-x) x}{\sqrt{1-x^2}} \, dx\)
3.44
\(\int \frac{x-x^2}{\sqrt{1-x^2}} \, dx\)
3.45
\(\int \frac{3+x^2}{-3+x^2} \, dx\)
3.46
\(\int \frac{-1+x^2}{1+x^2} \, dx\)
3.47
\(\int \frac{x^7 (A+B x+C x^2)}{(a+b x^2)^{9/2}} \, dx\)
3.48
\(\int \frac{x^6 (A+B x+C x^2)}{(a+b x^2)^{9/2}} \, dx\)
3.49
\(\int \frac{x^5 (A+B x+C x^2)}{(a+b x^2)^{9/2}} \, dx\)
3.50
\(\int \frac{x^4 (A+B x+C x^2)}{(a+b x^2)^{9/2}} \, dx\)
3.51
\(\int \frac{x^3 (A+B x+C x^2)}{(a+b x^2)^{9/2}} \, dx\)
3.52
\(\int \frac{x^2 (A+B x+C x^2)}{(a+b x^2)^{9/2}} \, dx\)
3.53
\(\int \frac{x (A+B x+C x^2)}{(a+b x^2)^{9/2}} \, dx\)
3.54
\(\int \frac{A+B x+C x^2}{(a+b x^2)^{9/2}} \, dx\)
3.55
\(\int \frac{A+B x+C x^2}{x (a+b x^2)^{9/2}} \, dx\)
3.56
\(\int \frac{A+B x+C x^2}{x^2 (a+b x^2)^{9/2}} \, dx\)
3.57
\(\int \frac{A+B x+C x^2}{x^3 (a+b x^2)^{9/2}} \, dx\)
3.58
\(\int \frac{A (c x)^m}{a+b x^2} \, dx\)
3.59
\(\int \frac{(c x)^m (A+B x)}{a+b x^2} \, dx\)
3.60
\(\int \frac{(c x)^m (A+C x^2)}{a+b x^2} \, dx\)
3.61
\(\int \frac{(c x)^m (A+B x+C x^2)}{a+b x^2} \, dx\)
3.62
\(\int x^3 (a+b x^2) (A+B x+C x^2+D x^3) \, dx\)
3.63
\(\int x^2 (a+b x^2) (A+B x+C x^2+D x^3) \, dx\)
3.64
\(\int x (a+b x^2) (A+B x+C x^2+D x^3) \, dx\)
3.65
\(\int (a+b x^2) (A+B x+C x^2+D x^3) \, dx\)
3.66
\(\int \frac{(a+b x^2) (A+B x+C x^2+D x^3)}{x} \, dx\)
3.67
\(\int \frac{(a+b x^2) (A+B x+C x^2+D x^3)}{x^2} \, dx\)
3.68
\(\int \frac{(a+b x^2) (A+B x+C x^2+D x^3)}{x^3} \, dx\)
3.69
\(\int \frac{(a+b x^2) (A+B x+C x^2+D x^3)}{x^4} \, dx\)
3.70
\(\int x^3 (a+b x^2)^2 (A+B x+C x^2+D x^3) \, dx\)
3.71
\(\int x^2 (a+b x^2)^2 (A+B x+C x^2+D x^3) \, dx\)
3.72
\(\int x (a+b x^2)^2 (A+B x+C x^2+D x^3) \, dx\)
3.73
\(\int (a+b x^2)^2 (A+B x+C x^2+D x^3) \, dx\)
3.74
\(\int \frac{(a+b x^2)^2 (A+B x+C x^2+D x^3)}{x} \, dx\)
3.75
\(\int \frac{(a+b x^2)^2 (A+B x+C x^2+D x^3)}{x^2} \, dx\)
3.76
\(\int \frac{(a+b x^2)^2 (A+B x+C x^2+D x^3)}{x^3} \, dx\)
3.77
\(\int \frac{(a+b x^2)^2 (A+B x+C x^2+D x^3)}{x^4} \, dx\)
3.78
\(\int x^3 (a+b x^2)^3 (A+B x+C x^2+D x^3) \, dx\)
3.79
\(\int x^2 (a+b x^2)^3 (A+B x+C x^2+D x^3) \, dx\)
3.80
\(\int x (a+b x^2)^3 (A+B x+C x^2+D x^3) \, dx\)
3.81
\(\int (a+b x^2)^3 (A+B x+C x^2+D x^3) \, dx\)
3.82
\(\int \frac{(a+b x^2)^3 (A+B x+C x^2+D x^3)}{x} \, dx\)
3.83
\(\int \frac{(a+b x^2)^3 (A+B x+C x^2+D x^3)}{x^2} \, dx\)
3.84
\(\int \frac{(a+b x^2)^3 (A+B x+C x^2+D x^3)}{x^3} \, dx\)
3.85
\(\int \frac{(a+b x^2)^3 (A+B x+C x^2+D x^3)}{x^4} \, dx\)
3.86
\(\int \frac{x^4 (A+B x+C x^2+D x^3)}{a+b x^2} \, dx\)
3.87
\(\int \frac{x^3 (A+B x+C x^2+D x^3)}{a+b x^2} \, dx\)
3.88
\(\int \frac{x^2 (A+B x+C x^2+D x^3)}{a+b x^2} \, dx\)
3.89
\(\int \frac{x (A+B x+C x^2+D x^3)}{a+b x^2} \, dx\)
3.90
\(\int \frac{A+B x+C x^2+D x^3}{a+b x^2} \, dx\)
3.91
\(\int \frac{A+B x+C x^2+D x^3}{x (a+b x^2)} \, dx\)
3.92
\(\int \frac{A+B x+C x^2+D x^3}{x^2 (a+b x^2)} \, dx\)
3.93
\(\int \frac{A+B x+C x^2+D x^3}{x^3 (a+b x^2)} \, dx\)
3.94
\(\int \frac{x^4 (A+B x+C x^2+D x^3)}{(a+b x^2)^2} \, dx\)
3.95
\(\int \frac{x^3 (A+B x+C x^2+D x^3)}{(a+b x^2)^2} \, dx\)
3.96
\(\int \frac{x^2 (A+B x+C x^2+D x^3)}{(a+b x^2)^2} \, dx\)
3.97
\(\int \frac{x (A+B x+C x^2+D x^3)}{(a+b x^2)^2} \, dx\)
3.98
\(\int \frac{A+B x+C x^2+D x^3}{(a+b x^2)^2} \, dx\)
3.99
\(\int \frac{A+B x+C x^2+D x^3}{x (a+b x^2)^2} \, dx\)
3.100
\(\int \frac{A+B x+C x^2+D x^3}{x^2 (a+b x^2)^2} \, dx\)
3.101
\(\int \frac{A+B x+C x^2+D x^3}{x^3 (a+b x^2)^2} \, dx\)
3.102
\(\int \frac{x^4 (A+B x+C x^2+D x^3)}{(a+b x^2)^3} \, dx\)
3.103
\(\int \frac{x^3 (A+B x+C x^2+D x^3)}{(a+b x^2)^3} \, dx\)
3.104
\(\int \frac{x^2 (A+B x+C x^2+D x^3)}{(a+b x^2)^3} \, dx\)
3.105
\(\int \frac{x (A+B x+C x^2+D x^3)}{(a+b x^2)^3} \, dx\)
3.106
\(\int \frac{A+B x+C x^2+D x^3}{(a+b x^2)^3} \, dx\)
3.107
\(\int \frac{A+B x+C x^2+D x^3}{x (a+b x^2)^3} \, dx\)
3.108
\(\int \frac{A+B x+C x^2+D x^3}{x^2 (a+b x^2)^3} \, dx\)
3.109
\(\int \frac{A+B x+C x^2+D x^3}{x^3 (a+b x^2)^3} \, dx\)
3.110
\(\int \frac{-x+4 x^3}{(5+x^2)^2} \, dx\)
3.111
\(\int \frac{-x+x^3}{\sqrt{-2+x^2}} \, dx\)
3.112
\(\int \frac{-x^2+2 x^4}{1+2 x^2} \, dx\)
3.113
\(\int \frac{x^3+x^4}{1+x^2} \, dx\)
3.114
\(\int \frac{x^6 (c+d x^2+e x^4+f x^6)}{a+b x^2} \, dx\)
3.115
\(\int \frac{x^4 (c+d x^2+e x^4+f x^6)}{a+b x^2} \, dx\)
3.116
\(\int \frac{x^2 (c+d x^2+e x^4+f x^6)}{a+b x^2} \, dx\)
3.117
\(\int \frac{c+d x^2+e x^4+f x^6}{a+b x^2} \, dx\)
3.118
\(\int \frac{c+d x^2+e x^4+f x^6}{x^2 (a+b x^2)} \, dx\)
3.119
\(\int \frac{c+d x^2+e x^4+f x^6}{x^4 (a+b x^2)} \, dx\)
3.120
\(\int \frac{c+d x^2+e x^4+f x^6}{x^6 (a+b x^2)} \, dx\)
3.121
\(\int \frac{c+d x^2+e x^4+f x^6}{x^8 (a+b x^2)} \, dx\)
3.122
\(\int \frac{c+d x^2+e x^4+f x^6}{x^{10} (a+b x^2)} \, dx\)
3.123
\(\int \frac{c+d x^2+e x^4+f x^6}{x^{12} (a+b x^2)} \, dx\)
3.124
\(\int \frac{x^6 (c+d x^2+e x^4+f x^6)}{(a+b x^2)^2} \, dx\)
3.125
\(\int \frac{x^4 (c+d x^2+e x^4+f x^6)}{(a+b x^2)^2} \, dx\)
3.126
\(\int \frac{x^2 (c+d x^2+e x^4+f x^6)}{(a+b x^2)^2} \, dx\)
3.127
\(\int \frac{c+d x^2+e x^4+f x^6}{(a+b x^2)^2} \, dx\)
3.128
\(\int \frac{c+d x^2+e x^4+f x^6}{x^2 (a+b x^2)^2} \, dx\)
3.129
\(\int \frac{c+d x^2+e x^4+f x^6}{x^4 (a+b x^2)^2} \, dx\)
3.130
\(\int \frac{c+d x^2+e x^4+f x^6}{x^6 (a+b x^2)^2} \, dx\)
3.131
\(\int \frac{c+d x^2+e x^4+f x^6}{x^8 (a+b x^2)^2} \, dx\)
3.132
\(\int \frac{c+d x^2+e x^4+f x^6}{x^{10} (a+b x^2)^2} \, dx\)
3.133
\(\int \frac{x^8 (c+d x^2+e x^4+f x^6)}{(a+b x^2)^3} \, dx\)
3.134
\(\int \frac{x^6 (c+d x^2+e x^4+f x^6)}{(a+b x^2)^3} \, dx\)
3.135
\(\int \frac{x^4 (c+d x^2+e x^4+f x^6)}{(a+b x^2)^3} \, dx\)
3.136
\(\int \frac{x^2 (c+d x^2+e x^4+f x^6)}{(a+b x^2)^3} \, dx\)
3.137
\(\int \frac{c+d x^2+e x^4+f x^6}{(a+b x^2)^3} \, dx\)
3.138
\(\int \frac{c+d x^2+e x^4+f x^6}{x^2 (a+b x^2)^3} \, dx\)
3.139
\(\int \frac{c+d x^2+e x^4+f x^6}{x^4 (a+b x^2)^3} \, dx\)
3.140
\(\int \frac{c+d x^2+e x^4+f x^6}{x^6 (a+b x^2)^3} \, dx\)
3.141
\(\int \frac{c+d x^2+e x^4+f x^6}{x^8 (a+b x^2)^3} \, dx\)
3.142
\(\int \frac{c+d x^2+e x^4+f x^6}{x^{10} (a+b x^2)^3} \, dx\)
3.143
\(\int \frac{x^5 (c+d x^2+e x^4+f x^6)}{\sqrt{a+b x^2}} \, dx\)
3.144
\(\int \frac{x^3 (c+d x^2+e x^4+f x^6)}{\sqrt{a+b x^2}} \, dx\)
3.145
\(\int \frac{x (c+d x^2+e x^4+f x^6)}{\sqrt{a+b x^2}} \, dx\)
3.146
\(\int \frac{c+d x^2+e x^4+f x^6}{x \sqrt{a+b x^2}} \, dx\)
3.147
\(\int \frac{c+d x^2+e x^4+f x^6}{x^3 \sqrt{a+b x^2}} \, dx\)
3.148
\(\int \frac{c+d x^2+e x^4+f x^6}{x^5 \sqrt{a+b x^2}} \, dx\)
3.149
\(\int \frac{c+d x^2+e x^4+f x^6}{x^7 \sqrt{a+b x^2}} \, dx\)
3.150
\(\int \frac{c+d x^2+e x^4+f x^6}{x^9 \sqrt{a+b x^2}} \, dx\)
3.151
\(\int \frac{x^4 (c+d x^2+e x^4+f x^6)}{\sqrt{a+b x^2}} \, dx\)
3.152
\(\int \frac{x^2 (c+d x^2+e x^4+f x^6)}{\sqrt{a+b x^2}} \, dx\)
3.153
\(\int \frac{c+d x^2+e x^4+f x^6}{\sqrt{a+b x^2}} \, dx\)
3.154
\(\int \frac{c+d x^2+e x^4+f x^6}{x^2 \sqrt{a+b x^2}} \, dx\)
3.155
\(\int \frac{c+d x^2+e x^4+f x^6}{x^4 \sqrt{a+b x^2}} \, dx\)
3.156
\(\int \frac{c+d x^2+e x^4+f x^6}{x^6 \sqrt{a+b x^2}} \, dx\)
3.157
\(\int \frac{c+d x^2+e x^4+f x^6}{x^8 \sqrt{a+b x^2}} \, dx\)
3.158
\(\int \frac{c+d x^2+e x^4+f x^6}{x^{10} \sqrt{a+b x^2}} \, dx\)
3.159
\(\int \frac{x^8 (A+B x^2+C x^4+D x^6)}{(a+b x^2)^{9/2}} \, dx\)
3.160
\(\int \frac{x^6 (A+B x^2+C x^4+D x^6)}{(a+b x^2)^{9/2}} \, dx\)
3.161
\(\int \frac{x^4 (A+B x^2+C x^4+D x^6)}{(a+b x^2)^{9/2}} \, dx\)
3.162
\(\int \frac{x^2 (A+B x^2+C x^4+D x^6)}{(a+b x^2)^{9/2}} \, dx\)
3.163
\(\int \frac{A+B x^2+C x^4+D x^6}{(a+b x^2)^{9/2}} \, dx\)
3.164
\(\int \frac{A+B x^2+C x^4+D x^6}{x^2 (a+b x^2)^{9/2}} \, dx\)
3.165
\(\int \frac{A+B x^2+C x^4+D x^6}{x^4 (a+b x^2)^{9/2}} \, dx\)
3.166
\(\int \frac{A+B x^2+C x^4+D x^6}{x^6 (a+b x^2)^{9/2}} \, dx\)
3.167
\(\int \frac{A+B x^2+C x^4+D x^6}{x^8 (a+b x^2)^{9/2}} \, dx\)
3.168
\(\int \frac{A+B x^2+C x^4+D x^6}{x^{10} (a+b x^2)^{9/2}} \, dx\)
3.169
\(\int \frac{c x^5+d x^7+e x^9+f x^{11}}{\sqrt{a+b x^2}} \, dx\)
3.170
\(\int \frac{c x^3+d x^5+e x^7+f x^9}{\sqrt{a+b x^2}} \, dx\)
3.171
\(\int \frac{c x+d x^3+e x^5+f x^7}{\sqrt{a+b x^2}} \, dx\)
3.172
\(\int \frac{x^2 (A+B x^2+C x^4+D x^6+F x^8)}{(a+b x^2)^{9/2}} \, dx\)
3.173
\(\int \frac{A+B x^2+C x^4+D x^6+F x^8}{(a+b x^2)^{9/2}} \, dx\)
3.174
\(\int \frac{A+B x^2+C x^4+D x^6+F x^8}{x^2 (a+b x^2)^{9/2}} \, dx\)
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