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