3.1 \(\int (a+a \sin (c+d x)) \tan ^5(c+d x) \, dx\)
 3.2 \(\int (a+a \sin (c+d x)) \tan ^3(c+d x) \, dx\)
 3.3 \(\int (a+a \sin (c+d x)) \tan (c+d x) \, dx\)
 3.4 \(\int \cot (c+d x) (a+a \sin (c+d x)) \, dx\)
 3.5 \(\int \cot ^3(c+d x) (a+a \sin (c+d x)) \, dx\)
 3.6 \(\int \cot ^5(c+d x) (a+a \sin (c+d x)) \, dx\)
 3.7 \(\int \cot ^7(c+d x) (a+a \sin (c+d x)) \, dx\)
 3.8 \(\int (a+a \sin (c+d x)) \tan ^6(c+d x) \, dx\)
 3.9 \(\int (a+a \sin (c+d x)) \tan ^4(c+d x) \, dx\)
 3.10 \(\int (a+a \sin (c+d x)) \tan ^2(c+d x) \, dx\)
 3.11 \(\int \cot ^2(c+d x) (a+a \sin (c+d x)) \, dx\)
 3.12 \(\int \cot ^4(c+d x) (a+a \sin (c+d x)) \, dx\)
 3.13 \(\int \cot ^6(c+d x) (a+a \sin (c+d x)) \, dx\)
 3.14 \(\int (a+a \sin (c+d x))^2 \tan ^5(c+d x) \, dx\)
 3.15 \(\int (a+a \sin (c+d x))^2 \tan ^3(c+d x) \, dx\)
 3.16 \(\int (a+a \sin (c+d x))^2 \tan (c+d x) \, dx\)
 3.17 \(\int \cot ^3(c+d x) (a+a \sin (c+d x))^2 \, dx\)
 3.18 \(\int \cot ^7(c+d x) (a+a \sin (c+d x))^2 \, dx\)
 3.19 \(\int (a+a \sin (c+d x))^2 \tan ^6(c+d x) \, dx\)
 3.20 \(\int (a+a \sin (c+d x))^2 \tan ^4(c+d x) \, dx\)
 3.21 \(\int (a+a \sin (c+d x))^2 \tan ^2(c+d x) \, dx\)
 3.22 \(\int (a+a \sin (c+d x))^2 \, dx\)
 3.23 \(\int \cot ^2(c+d x) (a+a \sin (c+d x))^2 \, dx\)
 3.24 \(\int \cot ^4(c+d x) (a+a \sin (c+d x))^2 \, dx\)
 3.25 \(\int (a+a \sin (c+d x))^3 \tan ^7(c+d x) \, dx\)
 3.26 \(\int (a+a \sin (c+d x))^3 \tan ^3(c+d x) \, dx\)
 3.27 \(\int (a+a \sin (c+d x))^3 \tan (c+d x) \, dx\)
 3.28 \(\int \cot ^3(c+d x) (a+a \sin (c+d x))^3 \, dx\)
 3.29 \(\int (a+a \sin (c+d x))^3 \tan ^6(c+d x) \, dx\)
 3.30 \(\int (a+a \sin (c+d x))^3 \tan ^4(c+d x) \, dx\)
 3.31 \(\int (a+a \sin (c+d x))^3 \tan ^2(c+d x) \, dx\)
 3.32 \(\int (a+a \sin (c+d x))^3 \, dx\)
 3.33 \(\int \cot ^2(c+d x) (a+a \sin (c+d x))^3 \, dx\)
 3.34 \(\int (a+a \sin (c+d x))^4 \tan ^5(c+d x) \, dx\)
 3.35 \(\int (a+a \sin (c+d x))^4 \tan ^3(c+d x) \, dx\)
 3.36 \(\int (a+a \sin (c+d x))^4 \tan (c+d x) \, dx\)
 3.37 \(\int \cot ^3(c+d x) (a+a \sin (c+d x))^4 \, dx\)
 3.38 \(\int (a+a \sin (c+d x))^4 \tan ^4(c+d x) \, dx\)
 3.39 \(\int (a+a \sin (c+d x))^4 \tan ^2(c+d x) \, dx\)
 3.40 \(\int (a+a \sin (c+d x))^4 \, dx\)
 3.41 \(\int \cot ^2(c+d x) (a+a \sin (c+d x))^4 \, dx\)
 3.42 \(\int \cot ^4(c+d x) (a+a \sin (c+d x))^4 \, dx\)
 3.43 \(\int \cot ^6(c+d x) (a+a \sin (c+d x))^4 \, dx\)
 3.44 \(\int \frac{\tan ^7(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.45 \(\int \frac{\tan ^5(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.46 \(\int \frac{\tan ^3(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.47 \(\int \frac{\tan (c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.48 \(\int \frac{\cot (c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.49 \(\int \frac{\cot ^3(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.50 \(\int \frac{\cot ^5(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.51 \(\int \frac{\cot ^7(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.52 \(\int \frac{\cot ^9(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.53 \(\int \frac{\tan ^6(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.54 \(\int \frac{\tan ^4(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.55 \(\int \frac{\tan ^2(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.56 \(\int \frac{1}{a+a \sin (c+d x)} \, dx\)
 3.57 \(\int \frac{\cot ^2(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.58 \(\int \frac{\cot ^4(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.59 \(\int \frac{\cot ^6(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.60 \(\int \frac{\cot ^8(c+d x)}{a+a \sin (c+d x)} \, dx\)
 3.61 \(\int \frac{\tan ^7(c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.62 \(\int \frac{\tan ^5(c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.63 \(\int \frac{\tan ^3(c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.64 \(\int \frac{\tan (c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.65 \(\int \frac{\cot (c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.66 \(\int \frac{\cot ^3(c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.67 \(\int \frac{\cot ^5(c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.68 \(\int \frac{\cot ^7(c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.69 \(\int \frac{\cot ^9(c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.70 \(\int \frac{\cot ^{11}(c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.71 \(\int \frac{\cot ^{13}(c+d x)}{(a+a \sin (c+d x))^2} \, dx\)
 3.72 \(\int \frac{\tan ^5(c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.73 \(\int \frac{\tan ^3(c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.74 \(\int \frac{\tan (c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.75 \(\int \frac{\cot (c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.76 \(\int \frac{\cot ^3(c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.77 \(\int \frac{\cot ^5(c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.78 \(\int \frac{\cot ^7(c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.79 \(\int \frac{\cot ^9(c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.80 \(\int \frac{\cot ^{11}(c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.81 \(\int \frac{\cot ^{13}(c+d x)}{(a+a \sin (c+d x))^3} \, dx\)
 3.82 \(\int \frac{\tan ^5(c+d x)}{(a+a \sin (c+d x))^4} \, dx\)
 3.83 \(\int \frac{\tan ^3(c+d x)}{(a+a \sin (c+d x))^4} \, dx\)
 3.84 \(\int \frac{\tan (c+d x)}{(a+a \sin (c+d x))^4} \, dx\)
 3.85 \(\int \frac{\cot ^3(c+d x)}{(a+a \sin (c+d x))^4} \, dx\)
 3.86 \(\int \frac{\cot ^7(c+d x)}{(a+a \sin (c+d x))^4} \, dx\)
 3.87 \(\int \frac{\tan ^2(c+d x)}{(a+a \sin (c+d x))^4} \, dx\)
 3.88 \(\int \frac{\cot ^2(c+d x)}{(a+a \sin (c+d x))^4} \, dx\)
 3.89 \(\int \frac{\cot ^4(c+d x)}{(a+a \sin (c+d x))^4} \, dx\)
 3.90 \(\int \frac{\cot ^6(c+d x)}{(a+a \sin (c+d x))^4} \, dx\)
 3.91 \(\int \sqrt{a+a \sin (e+f x)} \tan ^4(e+f x) \, dx\)
 3.92 \(\int \sqrt{a+a \sin (e+f x)} \tan ^2(e+f x) \, dx\)
 3.93 \(\int \cot ^2(e+f x) \sqrt{a+a \sin (e+f x)} \, dx\)
 3.94 \(\int \cot ^4(e+f x) \sqrt{a+a \sin (e+f x)} \, dx\)
 3.95 \(\int (a+a \sin (e+f x))^{3/2} \tan ^4(e+f x) \, dx\)
 3.96 \(\int (a+a \sin (e+f x))^{3/2} \tan ^2(e+f x) \, dx\)
 3.97 \(\int \cot ^2(e+f x) (a+a \sin (e+f x))^{3/2} \, dx\)
 3.98 \(\int \cot ^4(e+f x) (a+a \sin (e+f x))^{3/2} \, dx\)
 3.99 \(\int (a+a \sin (e+f x))^{5/2} \tan ^4(e+f x) \, dx\)
 3.100 \(\int (a+a \sin (e+f x))^{5/2} \tan ^2(e+f x) \, dx\)
 3.101 \(\int \cot ^2(e+f x) (a+a \sin (e+f x))^{5/2} \, dx\)
 3.102 \(\int \cot ^4(e+f x) (a+a \sin (e+f x))^{5/2} \, dx\)
 3.103 \(\int \frac{\tan ^4(e+f x)}{\sqrt{a+a \sin (e+f x)}} \, dx\)
 3.104 \(\int \frac{\tan ^2(e+f x)}{\sqrt{a+a \sin (e+f x)}} \, dx\)
 3.105 \(\int \frac{\cot ^2(e+f x)}{\sqrt{a+a \sin (e+f x)}} \, dx\)
 3.106 \(\int \frac{\cot ^4(e+f x)}{\sqrt{a+a \sin (e+f x)}} \, dx\)
 3.107 \(\int \frac{\tan ^4(e+f x)}{(a+a \sin (e+f x))^{3/2}} \, dx\)
 3.108 \(\int \frac{\tan ^2(e+f x)}{(a+a \sin (e+f x))^{3/2}} \, dx\)
 3.109 \(\int \frac{\cot ^2(e+f x)}{(a+a \sin (e+f x))^{3/2}} \, dx\)
 3.110 \(\int \frac{\cot ^4(e+f x)}{(a+a \sin (e+f x))^{3/2}} \, dx\)
 3.111 \(\int \frac{\tan ^4(e+f x)}{(a+a \sin (e+f x))^{5/2}} \, dx\)
 3.112 \(\int \frac{\tan ^2(e+f x)}{(a+a \sin (e+f x))^{5/2}} \, dx\)
 3.113 \(\int \frac{\cot ^2(e+f x)}{(a+a \sin (e+f x))^{5/2}} \, dx\)
 3.114 \(\int \frac{\cot ^4(e+f x)}{(a+a \sin (e+f x))^{5/2}} \, dx\)
 3.115 \(\int \sqrt [3]{a+a \sin (e+f x)} \tan ^4(e+f x) \, dx\)
 3.116 \(\int \sqrt [3]{a+a \sin (e+f x)} \tan ^2(e+f x) \, dx\)
 3.117 \(\int \cot ^2(e+f x) \sqrt [3]{a+a \sin (e+f x)} \, dx\)
 3.118 \(\int \cot ^4(e+f x) \sqrt [3]{a+a \sin (e+f x)} \, dx\)
 3.119 \(\int \frac{\tan ^4(e+f x)}{\sqrt [3]{a+a \sin (e+f x)}} \, dx\)
 3.120 \(\int \frac{\tan ^2(e+f x)}{\sqrt [3]{a+a \sin (e+f x)}} \, dx\)
 3.121 \(\int \frac{\cot ^2(e+f x)}{\sqrt [3]{a+a \sin (e+f x)}} \, dx\)
 3.122 \(\int \frac{\cot ^4(e+f x)}{\sqrt [3]{a+a \sin (e+f x)}} \, dx\)
 3.123 \(\int (a+a \sin (e+f x))^3 (g \tan (e+f x))^p \, dx\)
 3.124 \(\int (a+a \sin (e+f x))^2 (g \tan (e+f x))^p \, dx\)
 3.125 \(\int (a+a \sin (e+f x)) (g \tan (e+f x))^p \, dx\)
 3.126 \(\int \frac{(g \tan (e+f x))^p}{a+a \sin (e+f x)} \, dx\)
 3.127 \(\int \frac{(g \tan (e+f x))^p}{(a+a \sin (e+f x))^2} \, dx\)
 3.128 \(\int \frac{(g \tan (e+f x))^p}{(a+a \sin (e+f x))^3} \, dx\)
 3.129 \(\int (a+a \sin (e+f x))^m (g \tan (e+f x))^p \, dx\)
 3.130 \(\int (a+a \sin (e+f x))^m \tan ^3(e+f x) \, dx\)
 3.131 \(\int (a+a \sin (e+f x))^m \tan (e+f x) \, dx\)
 3.132 \(\int \cot (e+f x) (a+a \sin (e+f x))^m \, dx\)
 3.133 \(\int \cot ^3(e+f x) (a+a \sin (e+f x))^m \, dx\)
 3.134 \(\int \cot ^5(e+f x) (a+a \sin (e+f x))^m \, dx\)
 3.135 \(\int (a+a \sin (e+f x))^m \tan ^4(e+f x) \, dx\)
 3.136 \(\int (a+a \sin (e+f x))^m \tan ^2(e+f x) \, dx\)
 3.137 \(\int (a+a \sin (e+f x))^m \, dx\)
 3.138 \(\int \cot ^2(e+f x) (a+a \sin (e+f x))^m \, dx\)
 3.139 \(\int \cot ^4(e+f x) (a+a \sin (e+f x))^m \, dx\)
 3.140 \(\int (a+b \sin (c+d x)) \tan ^3(c+d x) \, dx\)
 3.141 \(\int (a+b \sin (c+d x)) \tan (c+d x) \, dx\)
 3.142 \(\int \cot (c+d x) (a+b \sin (c+d x)) \, dx\)
 3.143 \(\int \cot ^3(c+d x) (a+b \sin (c+d x)) \, dx\)
 3.144 \(\int \cot ^5(c+d x) (a+b \sin (c+d x)) \, dx\)
 3.145 \(\int (a+b \sin (c+d x)) \tan ^4(c+d x) \, dx\)
 3.146 \(\int (a+b \sin (c+d x)) \tan ^2(c+d x) \, dx\)
 3.147 \(\int \cot ^2(c+d x) (a+b \sin (c+d x)) \, dx\)
 3.148 \(\int \cot ^4(c+d x) (a+b \sin (c+d x)) \, dx\)
 3.149 \(\int \cot ^6(c+d x) (a+b \sin (c+d x)) \, dx\)
 3.150 \(\int (a+b \sin (c+d x))^2 \tan ^3(c+d x) \, dx\)
 3.151 \(\int (a+b \sin (c+d x))^2 \tan (c+d x) \, dx\)
 3.152 \(\int \cot (c+d x) (a+b \sin (c+d x))^2 \, dx\)
 3.153 \(\int \cot ^3(c+d x) (a+b \sin (c+d x))^2 \, dx\)
 3.154 \(\int \cot ^5(c+d x) (a+b \sin (c+d x))^2 \, dx\)
 3.155 \(\int (a+b \sin (c+d x))^2 \tan ^4(c+d x) \, dx\)
 3.156 \(\int (a+b \sin (c+d x))^2 \tan ^2(c+d x) \, dx\)
 3.157 \(\int \cot ^2(c+d x) (a+b \sin (c+d x))^2 \, dx\)
 3.158 \(\int \cot ^4(c+d x) (a+b \sin (c+d x))^2 \, dx\)
 3.159 \(\int \cot ^6(c+d x) (a+b \sin (c+d x))^2 \, dx\)
 3.160 \(\int (a+b \sin (c+d x))^3 \tan ^3(c+d x) \, dx\)
 3.161 \(\int (a+b \sin (c+d x))^3 \tan (c+d x) \, dx\)
 3.162 \(\int \cot (c+d x) (a+b \sin (c+d x))^3 \, dx\)
 3.163 \(\int \cot ^3(c+d x) (a+b \sin (c+d x))^3 \, dx\)
 3.164 \(\int \cot ^5(c+d x) (a+b \sin (c+d x))^3 \, dx\)
 3.165 \(\int (a+b \sin (c+d x))^3 \tan ^4(c+d x) \, dx\)
 3.166 \(\int (a+b \sin (c+d x))^3 \tan ^2(c+d x) \, dx\)
 3.167 \(\int \cot ^2(c+d x) (a+b \sin (c+d x))^3 \, dx\)
 3.168 \(\int \cot ^4(c+d x) (a+b \sin (c+d x))^3 \, dx\)
 3.169 \(\int \cot ^6(c+d x) (a+b \sin (c+d x))^3 \, dx\)
 3.170 \(\int \frac{\tan ^5(c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.171 \(\int \frac{\tan ^3(c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.172 \(\int \frac{\tan (c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.173 \(\int \frac{\cot (c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.174 \(\int \frac{\cot ^3(c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.175 \(\int \frac{\cot ^5(c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.176 \(\int \frac{\tan ^4(c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.177 \(\int \frac{\tan ^2(c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.178 \(\int \frac{\cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.179 \(\int \frac{\cot ^4(c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.180 \(\int \frac{\cot ^6(c+d x)}{a+b \sin (c+d x)} \, dx\)
 3.181 \(\int \frac{\tan ^5(c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.182 \(\int \frac{\tan ^3(c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.183 \(\int \frac{\tan (c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.184 \(\int \frac{\cot (c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.185 \(\int \frac{\cot ^3(c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.186 \(\int \frac{\cot ^5(c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.187 \(\int \frac{\tan ^4(c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.188 \(\int \frac{\tan ^2(c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.189 \(\int \frac{\cot ^2(c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.190 \(\int \frac{\cot ^4(c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.191 \(\int \frac{\cot ^6(c+d x)}{(a+b \sin (c+d x))^2} \, dx\)
 3.192 \(\int \frac{\tan ^5(c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.193 \(\int \frac{\tan ^3(c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.194 \(\int \frac{\tan (c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.195 \(\int \frac{\cot (c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.196 \(\int \frac{\cot ^3(c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.197 \(\int \frac{\cot ^5(c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.198 \(\int \frac{\tan ^4(c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.199 \(\int \frac{\tan ^2(c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.200 \(\int \frac{\cot ^2(c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.201 \(\int \frac{\cot ^4(c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.202 \(\int \frac{\cot ^6(c+d x)}{(a+b \sin (c+d x))^3} \, dx\)
 3.203 \(\int (a+b \sin (e+f x))^3 (g \tan (e+f x))^p \, dx\)
 3.204 \(\int (a+b \sin (e+f x))^2 (g \tan (e+f x))^p \, dx\)
 3.205 \(\int (a+b \sin (e+f x)) (g \tan (e+f x))^p \, dx\)
 3.206 \(\int \frac{(g \tan (e+f x))^p}{a+b \sin (e+f x)} \, dx\)
 3.207 \(\int \frac{(g \tan (e+f x))^p}{(a+b \sin (e+f x))^2} \, dx\)
 3.208 \(\int (a+b \sin (e+f x))^m (g \tan (e+f x))^p \, dx\)