3.12.1 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \cos (c+d x))} \, dx\) [1101]
3.12.2 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+b \cos (c+d x))} \, dx\) [1102]
3.12.3 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^2} \, dx\) [1103]
3.12.4 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^2} \, dx\) [1104]
3.12.5 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^2} \, dx\) [1105]
3.12.6 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {\cos (c+d x)} (a+b \cos (c+d x))^2} \, dx\) [1106]
3.12.7 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \cos (c+d x))^2} \, dx\) [1107]
3.12.8 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \cos (c+d x))^2} \, dx\) [1108]
3.12.9 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^3} \, dx\) [1109]
3.12.10 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^3} \, dx\) [1110]
3.12.11 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^3} \, dx\) [1111]
3.12.12 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^3} \, dx\) [1112]
3.12.13 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {\cos (c+d x)} (a+b \cos (c+d x))^3} \, dx\) [1113]
3.12.14 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \cos (c+d x))^3} \, dx\) [1114]
3.12.15 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \cos (c+d x))^3} \, dx\) [1115]
3.12.16 \(\int \sqrt {\cos (c+d x)} \sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [1116]
3.12.17 \(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1117]
3.12.18 \(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1118]
3.12.19 \(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1119]
3.12.20 \(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1120]
3.12.21 \(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [1121]
3.12.22 \(\int \sqrt {\cos (c+d x)} (a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [1122]
3.12.23 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1123]
3.12.24 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1124]
3.12.25 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1125]
3.12.26 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1126]
3.12.27 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [1127]
3.12.28 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [1128]
3.12.29 \(\int \sqrt {\cos (c+d x)} (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [1129]
3.12.30 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1130]
3.12.31 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1131]
3.12.32 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1132]
3.12.33 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1133]
3.12.34 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [1134]
3.12.35 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [1135]
3.12.36 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1136]
3.12.37 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1137]
3.12.38 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {\cos (c+d x)} \sqrt {a+b \cos (c+d x)}} \, dx\) [1138]
3.12.39 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+b \cos (c+d x)}} \, dx\) [1139]
3.12.40 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+b \cos (c+d x)}} \, dx\) [1140]
3.12.41 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {a+b \cos (c+d x)}} \, dx\) [1141]
3.12.42 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \sqrt {a+b \cos (c+d x)}} \, dx\) [1142]
3.12.43 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (a A+(A b+a B) \cos (c+d x)+b B \cos ^2(c+d x))}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1143]
3.12.44 \(\int \genfrac {}{}{}{}{a+a \cos (c+d x)+2 b \cos ^2(c+d x)}{\sqrt {\cos (c+d x)} \sqrt {a+b \cos (c+d x)}} \, dx\) [1144]
3.12.45 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1145]
3.12.46 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1146]
3.12.47 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {\cos (c+d x)} (a+b \cos (c+d x))^{3/2}} \, dx\) [1147]
3.12.48 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \cos (c+d x))^{3/2}} \, dx\) [1148]
3.12.49 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \cos (c+d x))^{3/2}} \, dx\) [1149]
3.12.50 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \cos (c+d x))^{3/2}} \, dx\) [1150]
3.12.51 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^{5/2}} \, dx\) [1151]
3.12.52 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^{5/2}} \, dx\) [1152]
3.12.53 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {\cos (c+d x)} (a+b \cos (c+d x))^{5/2}} \, dx\) [1153]
3.12.54 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \cos (c+d x))^{5/2}} \, dx\) [1154]
3.12.55 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \cos (c+d x))^{5/2}} \, dx\) [1155]
3.12.56 \(\int \cos ^m(c+d x) (a+b \cos (c+d x))^2 (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [1156]
3.12.57 \(\int \cos ^m(c+d x) (a+b \cos (c+d x)) (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [1157]
3.12.58 \(\int \genfrac {}{}{}{}{\cos ^m(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{a+b \cos (c+d x)} \, dx\) [1158]
3.12.59 \(\int \genfrac {}{}{}{}{\cos ^m(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(a+b \cos (c+d x))^2} \, dx\) [1159]
3.12.60 \(\int (a+a \cos (c+d x)) (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1160]
3.12.61 \(\int (a+a \cos (c+d x)) (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1161]
3.12.62 \(\int (a+a \cos (c+d x)) (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1162]
3.12.63 \(\int (a+a \cos (c+d x)) (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1163]
3.12.64 \(\int (a+a \cos (c+d x)) (A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1164]
3.12.65 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x)) (A+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1165]
3.12.66 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x)) (A+C \cos ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1166]
3.12.67 \(\int (a+a \cos (c+d x))^2 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1167]
3.12.68 \(\int (a+a \cos (c+d x))^2 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1168]
3.12.69 \(\int (a+a \cos (c+d x))^2 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1169]
3.12.70 \(\int (a+a \cos (c+d x))^2 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1170]
3.12.71 \(\int (a+a \cos (c+d x))^2 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1171]
3.12.72 \(\int (a+a \cos (c+d x))^2 (A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1172]
3.12.73 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x))^2 (A+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1173]
3.12.74 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x))^2 (A+C \cos ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1174]
3.12.75 \(\int (a+a \cos (c+d x))^3 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{13}{2}}(c+d x) \, dx\) [1175]
3.12.76 \(\int (a+a \cos (c+d x))^3 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1176]
3.12.77 \(\int (a+a \cos (c+d x))^3 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1177]
3.12.78 \(\int (a+a \cos (c+d x))^3 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1178]
3.12.79 \(\int (a+a \cos (c+d x))^3 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1179]
3.12.80 \(\int (a+a \cos (c+d x))^3 (A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1180]
3.12.81 \(\int (a+a \cos (c+d x))^3 (A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1181]
3.12.82 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x))^3 (A+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1182]
3.12.83 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x))^3 (A+C \cos ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1183]
3.12.84 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)}{a+a \cos (c+d x)} \, dx\) [1184]
3.12.85 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{a+a \cos (c+d x)} \, dx\) [1185]
3.12.86 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{a+a \cos (c+d x)} \, dx\) [1186]
3.12.87 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{a+a \cos (c+d x)} \, dx\) [1187]
3.12.88 \(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+a \cos (c+d x)) \sqrt {\sec (c+d x)}} \, dx\) [1188]
3.12.89 \(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+a \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1189]
3.12.90 \(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+a \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1190]
3.12.91 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+a \cos (c+d x))^2} \, dx\) [1191]
3.12.92 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+a \cos (c+d x))^2} \, dx\) [1192]
3.12.93 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{(a+a \cos (c+d x))^2} \, dx\) [1193]
3.12.94 \(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+a \cos (c+d x))^2 \sqrt {\sec (c+d x)}} \, dx\) [1194]
3.12.95 \(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+a \cos (c+d x))^2 \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1195]
3.12.96 \(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+a \cos (c+d x))^2 \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1196]
3.12.97 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+a \cos (c+d x))^3} \, dx\) [1197]
3.12.98 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+a \cos (c+d x))^3} \, dx\) [1198]
3.12.99 \(\int \genfrac {}{}{}{}{(A+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{(a+a \cos (c+d x))^3} \, dx\) [1199]
3.12.100 \(\int \genfrac {}{}{}{}{A+C \cos ^2(c+d x)}{(a+a \cos (c+d x))^3 \sqrt {\sec (c+d x)}} \, dx\) [1200]