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Chapter 3
Listing of integrals
3.1
\(\int (c+d x)^4 \cos (a+b x) \, dx\)
3.2
\(\int (c+d x)^3 \cos (a+b x) \, dx\)
3.3
\(\int (c+d x)^2 \cos (a+b x) \, dx\)
3.4
\(\int (c+d x) \cos (a+b x) \, dx\)
3.5
\(\int \frac {\cos (a+b x)}{c+d x} \, dx\)
3.6
\(\int \frac {\cos (a+b x)}{(c+d x)^2} \, dx\)
3.7
\(\int \frac {\cos (a+b x)}{(c+d x)^3} \, dx\)
3.8
\(\int \frac {\cos (a+b x)}{(c+d x)^4} \, dx\)
3.9
\(\int (c+d x)^4 \cos ^2(a+b x) \, dx\)
3.10
\(\int (c+d x)^3 \cos ^2(a+b x) \, dx\)
3.11
\(\int (c+d x)^2 \cos ^2(a+b x) \, dx\)
3.12
\(\int (c+d x) \cos ^2(a+b x) \, dx\)
3.13
\(\int \frac {\cos ^2(a+b x)}{c+d x} \, dx\)
3.14
\(\int \frac {\cos ^2(a+b x)}{(c+d x)^2} \, dx\)
3.15
\(\int \frac {\cos ^2(a+b x)}{(c+d x)^3} \, dx\)
3.16
\(\int (c+d x)^4 \cos ^3(a+b x) \, dx\)
3.17
\(\int (c+d x)^3 \cos ^3(a+b x) \, dx\)
3.18
\(\int (c+d x)^2 \cos ^3(a+b x) \, dx\)
3.19
\(\int (c+d x) \cos ^3(a+b x) \, dx\)
3.20
\(\int \frac {\cos ^3(a+b x)}{c+d x} \, dx\)
3.21
\(\int \frac {\cos ^3(a+b x)}{(c+d x)^2} \, dx\)
3.22
\(\int \frac {\cos ^3(a+b x)}{(c+d x)^3} \, dx\)
3.23
\(\int x^3 \cos ^4(a+b x) \, dx\)
3.24
\(\int x^2 \cos ^4(a+b x) \, dx\)
3.25
\(\int x \cos ^4(a+b x) \, dx\)
3.26
\(\int \frac {\cos ^4(a+b x)}{x} \, dx\)
3.27
\(\int \frac {\cos ^4(a+b x)}{x^2} \, dx\)
3.28
\(\int \frac {\cos ^4(a+b x)}{x^3} \, dx\)
3.29
\(\int (c+d x)^3 \sec (a+b x) \, dx\)
3.30
\(\int (c+d x)^2 \sec (a+b x) \, dx\)
3.31
\(\int (c+d x) \sec (a+b x) \, dx\)
3.32
\(\int \frac {\sec (a+b x)}{c+d x} \, dx\)
3.33
\(\int (c+d x)^3 \sec ^2(a+b x) \, dx\)
3.34
\(\int (c+d x)^2 \sec ^2(a+b x) \, dx\)
3.35
\(\int (c+d x) \sec ^2(a+b x) \, dx\)
3.36
\(\int \frac {\sec ^2(a+b x)}{c+d x} \, dx\)
3.37
\(\int (c+d x)^3 \sec ^3(a+b x) \, dx\)
3.38
\(\int (c+d x)^2 \sec ^3(a+b x) \, dx\)
3.39
\(\int (c+d x) \sec ^3(a+b x) \, dx\)
3.40
\(\int \frac {\sec ^2(a+b x)}{c+d x} \, dx\)
3.41
\(\int (c+d x)^{5/2} \cos (a+b x) \, dx\)
3.42
\(\int (c+d x)^{3/2} \cos (a+b x) \, dx\)
3.43
\(\int \sqrt {c+d x} \cos (a+b x) \, dx\)
3.44
\(\int \frac {\cos (a+b x)}{\sqrt {c+d x}} \, dx\)
3.45
\(\int \frac {\cos (a+b x)}{(c+d x)^{3/2}} \, dx\)
3.46
\(\int \frac {\cos (a+b x)}{(c+d x)^{5/2}} \, dx\)
3.47
\(\int \frac {\cos (a+b x)}{(c+d x)^{7/2}} \, dx\)
3.48
\(\int (c+d x)^{5/2} \cos ^2(a+b x) \, dx\)
3.49
\(\int (c+d x)^{3/2} \cos ^2(a+b x) \, dx\)
3.50
\(\int \sqrt {c+d x} \cos ^2(a+b x) \, dx\)
3.51
\(\int \frac {\cos ^2(a+b x)}{\sqrt {c+d x}} \, dx\)
3.52
\(\int \frac {\cos ^2(a+b x)}{(c+d x)^{3/2}} \, dx\)
3.53
\(\int \frac {\cos ^2(a+b x)}{(c+d x)^{5/2}} \, dx\)
3.54
\(\int \frac {\cos ^2(a+b x)}{(c+d x)^{7/2}} \, dx\)
3.55
\(\int \frac {\cos ^2(a+b x)}{(c+d x)^{9/2}} \, dx\)
3.56
\(\int (c+d x)^{5/2} \cos ^3(a+b x) \, dx\)
3.57
\(\int (c+d x)^{3/2} \cos ^3(a+b x) \, dx\)
3.58
\(\int \sqrt {c+d x} \cos ^3(a+b x) \, dx\)
3.59
\(\int \frac {\cos ^3(a+b x)}{\sqrt {c+d x}} \, dx\)
3.60
\(\int \frac {\cos ^3(a+b x)}{(c+d x)^{3/2}} \, dx\)
3.61
\(\int \frac {\cos ^3(a+b x)}{(c+d x)^{5/2}} \, dx\)
3.62
\(\int \frac {\cos ^3(a+b x)}{(c+d x)^{7/2}} \, dx\)
3.63
\(\int x^{3/2} \cos (x) \, dx\)
3.64
\(\int \sqrt {x} \cos (x) \, dx\)
3.65
\(\int \frac {\cos (x)}{\sqrt {x}} \, dx\)
3.66
\(\int \frac {\cos (x)}{x^{3/2}} \, dx\)
3.67
\(\int (c+d x)^{4/3} \cos (a+b x) \, dx\)
3.68
\(\int (c+d x)^{2/3} \cos (a+b x) \, dx\)
3.69
\(\int \sqrt [3]{c+d x} \cos (a+b x) \, dx\)
3.70
\(\int \frac {\cos (a+b x)}{\sqrt [3]{c+d x}} \, dx\)
3.71
\(\int \frac {\cos (a+b x)}{(c+d x)^{2/3}} \, dx\)
3.72
\(\int \frac {\cos (a+b x)}{(c+d x)^{4/3}} \, dx\)
3.73
\(\int \frac {\cos (a+b x)}{(c+d x)^{5/3}} \, dx\)
3.74
\(\int \frac {\cos (a+b x)}{(c+d x)^{7/3}} \, dx\)
3.75
\(\int x \sqrt {\cos (a+b x)} \, dx\)
3.76
\(\int \sqrt {\cos (a+b x)} \, dx\)
3.77
\(\int \frac {\sqrt {\cos (a+b x)}}{x} \, dx\)
3.78
\(\int x \cos ^{\frac {3}{2}}(a+b x) \, dx\)
3.79
\(\int \cos ^{\frac {3}{2}}(a+b x) \, dx\)
3.80
\(\int \frac {\cos ^{\frac {3}{2}}(a+b x)}{x} \, dx\)
3.81
\(\int (-\frac {x}{3 \sqrt {\cos (a+b x)}}+x \cos ^{\frac {3}{2}}(a+b x)) \, dx\)
3.82
\(\int \frac {\cos ^{\frac {3}{2}}(x)}{x^3} \, dx\)
3.83
\(\int \frac {x}{\sqrt {\cos (a+b x)}} \, dx\)
3.84
\(\int \frac {1}{\sqrt {\cos (a+b x)}} \, dx\)
3.85
\(\int \frac {1}{x \sqrt {\cos (a+b x)}} \, dx\)
3.86
\(\int \frac {x}{\cos ^{\frac {3}{2}}(a+b x)} \, dx\)
3.87
\(\int \frac {1}{\cos ^{\frac {3}{2}}(a+b x)} \, dx\)
3.88
\(\int \frac {1}{x \cos ^{\frac {3}{2}}(a+b x)} \, dx\)
3.89
\(\int (\frac {x}{\cos ^{\frac {3}{2}}(a+b x)}+x \sqrt {\cos (a+b x)}) \, dx\)
3.90
\(\int (\frac {x}{\cos ^{\frac {3}{2}}(x)}+x \sqrt {\cos (x)}) \, dx\)
3.91
\(\int (\frac {x}{\cos ^{\frac {5}{2}}(x)}-\frac {x}{3 \sqrt {\cos (x)}}) \, dx\)
3.92
\(\int (\frac {x}{\cos ^{\frac {7}{2}}(x)}+\frac {3}{5} x \sqrt {\cos (x)}) \, dx\)
3.93
\(\int (\frac {x^2}{\cos ^{\frac {3}{2}}(x)}+x^2 \sqrt {\cos (x)}) \, dx\)
3.94
\(\int (\frac {x}{\sec ^{\frac {3}{2}}(x)}-\frac {1}{3} x \sqrt {\sec (x)}) \, dx\)
3.95
\(\int (\frac {x}{\sec ^{\frac {5}{2}}(x)}-\frac {3 x}{5 \sqrt {\sec (x)}}) \, dx\)
3.96
\(\int (\frac {x}{\sec ^{\frac {7}{2}}(x)}-\frac {5}{21} x \sqrt {\sec (x)}) \, dx\)
3.97
\(\int (\frac {x^2}{\sec ^{\frac {3}{2}}(x)}-\frac {1}{3} x^2 \sqrt {\sec (x)}) \, dx\)
3.98
\(\int (c+d x)^m (b \cos (e+f x))^n \, dx\)
3.99
\(\int (c+d x)^m \cos ^3(a+b x) \, dx\)
3.100
\(\int (c+d x)^m \cos ^2(a+b x) \, dx\)
3.101
\(\int (c+d x)^m \cos (a+b x) \, dx\)
3.102
\(\int (c+d x)^m \sec (a+b x) \, dx\)
3.103
\(\int (c+d x)^m \sec ^2(a+b x) \, dx\)
3.104
\(\int x^{3+m} \cos (a+b x) \, dx\)
3.105
\(\int x^{2+m} \cos (a+b x) \, dx\)
3.106
\(\int x^{1+m} \cos (a+b x) \, dx\)
3.107
\(\int x^m \cos (a+b x) \, dx\)
3.108
\(\int x^{-1+m} \cos (a+b x) \, dx\)
3.109
\(\int x^{-2+m} \cos (a+b x) \, dx\)
3.110
\(\int x^{-3+m} \cos (a+b x) \, dx\)
3.111
\(\int x^{3+m} \cos ^2(a+b x) \, dx\)
3.112
\(\int x^{2+m} \cos ^2(a+b x) \, dx\)
3.113
\(\int x^{1+m} \cos ^2(a+b x) \, dx\)
3.114
\(\int x^m \cos ^2(a+b x) \, dx\)
3.115
\(\int x^{-1+m} \cos ^2(a+b x) \, dx\)
3.116
\(\int x^{-2+m} \cos ^2(a+b x) \, dx\)
3.117
\(\int x^{-3+m} \cos ^2(a+b x) \, dx\)
3.118
\(\int (c+d x)^3 (a+a \cos (e+f x)) \, dx\)
3.119
\(\int (c+d x)^2 (a+a \cos (e+f x)) \, dx\)
3.120
\(\int (c+d x) (a+a \cos (e+f x)) \, dx\)
3.121
\(\int \frac {a+a \cos (e+f x)}{c+d x} \, dx\)
3.122
\(\int \frac {a+a \cos (e+f x)}{(c+d x)^2} \, dx\)
3.123
\(\int (c+d x)^3 (a+a \cos (e+f x))^2 \, dx\)
3.124
\(\int (c+d x)^2 (a+a \cos (e+f x))^2 \, dx\)
3.125
\(\int (c+d x) (a+a \cos (e+f x))^2 \, dx\)
3.126
\(\int \frac {(a+a \cos (e+f x))^2}{c+d x} \, dx\)
3.127
\(\int \frac {(a+a \cos (e+f x))^2}{(c+d x)^2} \, dx\)
3.128
\(\int \frac {(c+d x)^3}{a+a \cos (e+f x)} \, dx\)
3.129
\(\int \frac {(c+d x)^2}{a+a \cos (e+f x)} \, dx\)
3.130
\(\int \frac {c+d x}{a+a \cos (e+f x)} \, dx\)
3.131
\(\int \frac {1}{(c+d x) (a+a \cos (e+f x))} \, dx\)
3.132
\(\int \frac {1}{(c+d x)^2 (a+a \cos (e+f x))} \, dx\)
3.133
\(\int \frac {(c+d x)^3}{(a+a \cos (e+f x))^2} \, dx\)
3.134
\(\int \frac {(c+d x)^2}{(a+a \cos (e+f x))^2} \, dx\)
3.135
\(\int \frac {c+d x}{(a+a \cos (e+f x))^2} \, dx\)
3.136
\(\int \frac {1}{(c+d x) (a+a \cos (e+f x))^2} \, dx\)
3.137
\(\int \frac {1}{(c+d x)^2 (a+a \cos (e+f x))^2} \, dx\)
3.138
\(\int \frac {(c+d x)^3}{a-a \cos (e+f x)} \, dx\)
3.139
\(\int \frac {(c+d x)^2}{a-a \cos (e+f x)} \, dx\)
3.140
\(\int \frac {c+d x}{a-a \cos (e+f x)} \, dx\)
3.141
\(\int \frac {1}{(c+d x) (a-a \cos (e+f x))} \, dx\)
3.142
\(\int \frac {1}{(c+d x)^2 (a-a \cos (e+f x))} \, dx\)
3.143
\(\int x^3 \sqrt {a+a \cos (c+d x)} \, dx\)
3.144
\(\int x^2 \sqrt {a+a \cos (c+d x)} \, dx\)
3.145
\(\int x \sqrt {a+a \cos (c+d x)} \, dx\)
3.146
\(\int \sqrt {a+a \cos (c+d x)} \, dx\)
3.147
\(\int \frac {\sqrt {a+a \cos (c+d x)}}{x} \, dx\)
3.148
\(\int \frac {\sqrt {a+a \cos (c+d x)}}{x^2} \, dx\)
3.149
\(\int \frac {\sqrt {a+a \cos (c+d x)}}{x^3} \, dx\)
3.150
\(\int x^3 \sqrt {a+a \cos (x)} \, dx\)
3.151
\(\int x^2 \sqrt {a+a \cos (x)} \, dx\)
3.152
\(\int x \sqrt {a+a \cos (x)} \, dx\)
3.153
\(\int \sqrt {a+a \cos (x)} \, dx\)
3.154
\(\int \frac {\sqrt {a+a \cos (x)}}{x} \, dx\)
3.155
\(\int \frac {\sqrt {a+a \cos (x)}}{x^2} \, dx\)
3.156
\(\int \frac {\sqrt {a+a \cos (x)}}{x^3} \, dx\)
3.157
\(\int x^3 \sqrt {a-a \cos (x)} \, dx\)
3.158
\(\int x^2 \sqrt {a-a \cos (x)} \, dx\)
3.159
\(\int x \sqrt {a-a \cos (x)} \, dx\)
3.160
\(\int \sqrt {a-a \cos (x)} \, dx\)
3.161
\(\int \frac {\sqrt {a-a \cos (x)}}{x} \, dx\)
3.162
\(\int \frac {\sqrt {a-a \cos (x)}}{x^2} \, dx\)
3.163
\(\int \frac {\sqrt {a-a \cos (x)}}{x^3} \, dx\)
3.164
\(\int x^3 (a+a \cos (x))^{3/2} \, dx\)
3.165
\(\int x^2 (a+a \cos (x))^{3/2} \, dx\)
3.166
\(\int x (a+a \cos (x))^{3/2} \, dx\)
3.167
\(\int \frac {(a+a \cos (x))^{3/2}}{x} \, dx\)
3.168
\(\int \frac {(a+a \cos (x))^{3/2}}{x^2} \, dx\)
3.169
\(\int \frac {(a+a \cos (x))^{3/2}}{x^3} \, dx\)
3.170
\(\int \frac {x^3}{\sqrt {a+a \cos (c+d x)}} \, dx\)
3.171
\(\int \frac {x^2}{\sqrt {a+a \cos (c+d x)}} \, dx\)
3.172
\(\int \frac {x}{\sqrt {a+a \cos (c+d x)}} \, dx\)
3.173
\(\int \frac {1}{\sqrt {a+a \cos (c+d x)}} \, dx\)
3.174
\(\int \frac {1}{x \sqrt {a+a \cos (c+d x)}} \, dx\)
3.175
\(\int \frac {x^3}{\sqrt {a-a \cos (x)}} \, dx\)
3.176
\(\int \frac {x^2}{\sqrt {a-a \cos (x)}} \, dx\)
3.177
\(\int \frac {x}{\sqrt {a-a \cos (x)}} \, dx\)
3.178
\(\int \frac {1}{\sqrt {a-a \cos (x)}} \, dx\)
3.179
\(\int \frac {1}{x \sqrt {a-a \cos (x)}} \, dx\)
3.180
\(\int \frac {x^3}{(a+a \cos (x))^{3/2}} \, dx\)
3.181
\(\int \frac {x^2}{(a+a \cos (x))^{3/2}} \, dx\)
3.182
\(\int \frac {x}{(a+a \cos (x))^{3/2}} \, dx\)
3.183
\(\int \frac {1}{x (a+a \cos (x))^{3/2}} \, dx\)
3.184
\(\int \frac {\sqrt [3]{a+a \cos (c+d x)}}{x} \, dx\)
3.185
\(\int \frac {x^3}{a+b \cos (x)} \, dx\)
3.186
\(\int \frac {x^2}{a+b \cos (c+d x)} \, dx\)
3.187
\(\int \frac {x}{a+b \cos (c+d x)} \, dx\)
3.188
\(\int \frac {1}{x (a+b \cos (x))} \, dx\)
3.189
\(\int \frac {e+f x}{(a+b \cos (c+d x))^2} \, dx\)
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