3.11.1 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1001]
  3.11.2 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [1002]
  3.11.3 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [1003]
  3.11.4 \(\int \sqrt {\sec (c+d x)} (a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1004]
  3.11.5 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1005]
  3.11.6 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1006]
  3.11.7 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1007]
  3.11.8 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1008]
  3.11.9 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [1009]
  3.11.10 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [1010]
  3.11.11 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{13}{2}}(c+d x)} \, dx\) [1011]
  3.11.12 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [1012]
  3.11.13 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [1013]
  3.11.14 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [1014]
  3.11.15 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} (a+b \sec (c+d x))} \, dx\) [1015]
  3.11.16 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))} \, dx\) [1016]
  3.11.17 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))} \, dx\) [1017]
  3.11.18 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \sec (c+d x))} \, dx\) [1018]
  3.11.19 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [1019]
  3.11.20 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [1020]
  3.11.21 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [1021]
  3.11.22 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} (a+b \sec (c+d x))^2} \, dx\) [1022]
  3.11.23 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^2} \, dx\) [1023]
  3.11.24 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^2} \, dx\) [1024]
  3.11.25 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [1025]
  3.11.26 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [1026]
  3.11.27 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [1027]
  3.11.28 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [1028]
  3.11.29 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} (a+b \sec (c+d x))^3} \, dx\) [1029]
  3.11.30 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^3} \, dx\) [1030]
  3.11.31 \(\int \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1031]
  3.11.32 \(\int \sqrt {\sec (c+d x)} \sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1032]
  3.11.33 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1033]
  3.11.34 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1034]
  3.11.35 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1035]
  3.11.36 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1036]
  3.11.37 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [1037]
  3.11.38 \(\int \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1038]
  3.11.39 \(\int \sqrt {\sec (c+d x)} (a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1039]
  3.11.40 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1040]
  3.11.41 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1041]
  3.11.42 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1042]
  3.11.43 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1043]
  3.11.44 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [1044]
  3.11.45 \(\int \sqrt {\sec (c+d x)} (a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1045]
  3.11.46 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1046]
  3.11.47 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1047]
  3.11.48 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1048]
  3.11.49 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1049]
  3.11.50 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [1050]
  3.11.51 \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [1051]
  3.11.52 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+b \sec (c+d x)}} \, dx\) [1052]
  3.11.53 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+b \sec (c+d x)}} \, dx\) [1053]
  3.11.54 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} \sqrt {a+b \sec (c+d x)}} \, dx\) [1054]
  3.11.55 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+b \sec (c+d x)}} \, dx\) [1055]
  3.11.56 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+b \sec (c+d x)}} \, dx\) [1056]
  3.11.57 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {a+b \sec (c+d x)}} \, dx\) [1057]
  3.11.58 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (a A+(A b+a B) \sec (c+d x)+b B \sec ^2(c+d x))}{\sqrt {a+b \sec (c+d x)}} \, dx\) [1058]
  3.11.59 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{3/2}} \, dx\) [1059]
  3.11.60 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{3/2}} \, dx\) [1060]
  3.11.61 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} (a+b \sec (c+d x))^{3/2}} \, dx\) [1061]
  3.11.62 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^{3/2}} \, dx\) [1062]
  3.11.63 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^{3/2}} \, dx\) [1063]
  3.11.64 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{5/2}} \, dx\) [1064]
  3.11.65 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{5/2}} \, dx\) [1065]
  3.11.66 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{5/2}} \, dx\) [1066]
  3.11.67 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} (a+b \sec (c+d x))^{5/2}} \, dx\) [1067]
  3.11.68 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^{5/2}} \, dx\) [1068]
  3.11.69 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^{5/2}} \, dx\) [1069]
  3.11.70 \(\int (a+b \sec (c+d x))^{2/3} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1070]
  3.11.71 \(\int \sqrt [3]{a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1071]
  3.11.72 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt [3]{a+b \sec (c+d x)}} \, dx\) [1072]
  3.11.73 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(a+b \sec (c+d x))^{2/3}} \, dx\) [1073]
  3.11.74 \(\int (a+b \sec (c+d x))^m (a b B-a^2 C+b^2 B \sec (c+d x)+b^2 C \sec ^2(c+d x)) \, dx\) [1074]
  3.11.75 \(\int \cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (A+C \sec ^2(c+d x)) \, dx\) [1075]
  3.11.76 \(\int \cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (A+C \sec ^2(c+d x)) \, dx\) [1076]
  3.11.77 \(\int \cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+C \sec ^2(c+d x)) \, dx\) [1077]
  3.11.78 \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+C \sec ^2(c+d x)) \, dx\) [1078]
  3.11.79 \(\int \sqrt {\cos (c+d x)} (A+C \sec ^2(c+d x)) \, dx\) [1079]
  3.11.80 \(\int \genfrac {}{}{}{}{A+C \sec ^2(c+d x)}{\sqrt {\cos (c+d x)}} \, dx\) [1080]
  3.11.81 \(\int \genfrac {}{}{}{}{A+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1081]
  3.11.82 \(\int \genfrac {}{}{}{}{A+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [1082]
  3.11.83 \(\int \cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+a \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [1083]
  3.11.84 \(\int \cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+a \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [1084]
  3.11.85 \(\int \cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+a \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [1085]
  3.11.86 \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+a \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [1086]
  3.11.87 \(\int \sqrt {\cos (c+d x)} (a+a \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [1087]
  3.11.88 \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x)) (A+C \sec ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1088]
  3.11.89 \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x)) (A+C \sec ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1089]
  3.11.90 \(\int \cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x) (a+a \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [1090]
  3.11.91 \(\int \cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+a \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [1091]
  3.11.92 \(\int \cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+a \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [1092]
  3.11.93 \(\int \cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+a \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [1093]
  3.11.94 \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+a \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [1094]
  3.11.95 \(\int \sqrt {\cos (c+d x)} (a+a \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [1095]
  3.11.96 \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^2 (A+C \sec ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1096]
  3.11.97 \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^2 (A+C \sec ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1097]
  3.11.98 \(\int \cos ^{\genfrac {}{}{}{}{13}{2}}(c+d x) (a+a \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [1098]
  3.11.99 \(\int \cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x) (a+a \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [1099]
  3.11.100 \(\int \cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+a \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [1100]