3.7.1 \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [601]
  3.7.2 \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [602]
  3.7.3 \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [603]
  3.7.4 \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{13}{2}}(c+d x)} \, dx\) [604]
  3.7.5 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+a \sec (c+d x)}} \, dx\) [605]
  3.7.6 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+a \sec (c+d x)}} \, dx\) [606]
  3.7.7 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+a \sec (c+d x)}} \, dx\) [607]
  3.7.8 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}} \, dx\) [608]
  3.7.9 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \, dx\) [609]
  3.7.10 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \, dx\) [610]
  3.7.11 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \, dx\) [611]
  3.7.12 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (a A+(A b+a B) \sec (c+d x)+b B \sec ^2(c+d x))}{\sqrt {a+a \sec (c+d x)}} \, dx\) [612]
  3.7.13 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx\) [613]
  3.7.14 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx\) [614]
  3.7.15 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx\) [615]
  3.7.16 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{3/2}} \, dx\) [616]
  3.7.17 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx\) [617]
  3.7.18 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx\) [618]
  3.7.19 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{5/2}} \, dx\) [619]
  3.7.20 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{5/2}} \, dx\) [620]
  3.7.21 \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{5/2}} \, dx\) [621]
  3.7.22 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{5/2}} \, dx\) [622]
  3.7.23 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+a \sec (c+d x))^{5/2}} \, dx\) [623]
  3.7.24 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+a \sec (c+d x))^{5/2}} \, dx\) [624]
  3.7.25 \(\int (a+a \sec (c+d x))^{2/3} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [625]
  3.7.26 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt [3]{a+a \sec (c+d x)}} \, dx\) [626]
  3.7.27 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(a+a \sec (c+d x))^{4/3}} \, dx\) [627]
  3.7.28 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(a+a \sec (c+d x))^{7/3}} \, dx\) [628]
  3.7.29 \(\int (a+a \sec (c+d x))^{4/3} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [629]
  3.7.30 \(\int \sqrt [3]{a+a \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [630]
  3.7.31 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(a+a \sec (c+d x))^{2/3}} \, dx\) [631]
  3.7.32 \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(a+a \sec (c+d x))^{5/3}} \, dx\) [632]
  3.7.33 \(\int \sec ^m(c+d x) (a+a \sec (c+d x))^n (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [633]
  3.7.34 \(\int \sec ^{-1-n}(c+d x) (a+a \sec (c+d x))^n (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [634]
  3.7.35 \(\int (\genfrac {}{}{}{}{\sec ^{-n}(c+d x) (a+a \sec (c+d x))^n (-a (B+A n+B n)-a C (1+n) \sec (c+d x))}{a (1+n)}+\sec ^{-1-n}(c+d x) (a+a \sec (c+d x))^n (A+B \sec (c+d x)+C \sec ^2(c+d x))) \, dx\) [635]
  3.7.36 \(\int (a+a \sec (c+d x))^m (B-C+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [636]
  3.7.37 \(\int \sec ^3(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [637]
  3.7.38 \(\int \sec ^2(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [638]
  3.7.39 \(\int \sec (c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [639]
  3.7.40 \(\int (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [640]
  3.7.41 \(\int \cos (c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [641]
  3.7.42 \(\int \cos ^2(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [642]
  3.7.43 \(\int \cos ^3(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [643]
  3.7.44 \(\int \cos ^4(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [644]
  3.7.45 \(\int \cos ^5(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [645]
  3.7.46 \(\int \sec ^2(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [646]
  3.7.47 \(\int \sec (c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [647]
  3.7.48 \(\int (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [648]
  3.7.49 \(\int \cos (c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [649]
  3.7.50 \(\int \cos ^2(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [650]
  3.7.51 \(\int \cos ^3(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [651]
  3.7.52 \(\int \cos ^4(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [652]
  3.7.53 \(\int \cos ^5(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [653]
  3.7.54 \(\int \sec ^2(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [654]
  3.7.55 \(\int \sec (c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [655]
  3.7.56 \(\int (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [656]
  3.7.57 \(\int \cos (c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [657]
  3.7.58 \(\int \cos ^2(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [658]
  3.7.59 \(\int \cos ^3(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [659]
  3.7.60 \(\int \cos ^4(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [660]
  3.7.61 \(\int \cos ^5(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [661]
  3.7.62 \(\int \cos ^6(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [662]
  3.7.63 \(\int \sec ^2(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [663]
  3.7.64 \(\int \sec (c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [664]
  3.7.65 \(\int (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [665]
  3.7.66 \(\int \cos (c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [666]
  3.7.67 \(\int \cos ^2(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [667]
  3.7.68 \(\int \cos ^3(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [668]
  3.7.69 \(\int \cos ^4(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [669]
  3.7.70 \(\int \cos ^5(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [670]
  3.7.71 \(\int \cos ^6(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [671]
  3.7.72 \(\int \cos ^7(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [672]
  3.7.73 \(\int (a+b \sec (c+d x))^3 (a^2-b^2 \sec ^2(c+d x)) \, dx\) [673]
  3.7.74 \(\int (a+b \sec (c+d x))^2 (a^2-b^2 \sec ^2(c+d x)) \, dx\) [674]
  3.7.75 \(\int (a+b \sec (c+d x)) (a^2-b^2 \sec ^2(c+d x)) \, dx\) [675]
  3.7.76 \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [676]
  3.7.77 \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [677]
  3.7.78 \(\int \genfrac {}{}{}{}{\sec (c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [678]
  3.7.79 \(\int \genfrac {}{}{}{}{A+C \sec ^2(c+d x)}{a+b \sec (c+d x)} \, dx\) [679]
  3.7.80 \(\int \genfrac {}{}{}{}{\cos (c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [680]
  3.7.81 \(\int \genfrac {}{}{}{}{\cos ^2(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [681]
  3.7.82 \(\int \genfrac {}{}{}{}{\cos ^3(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [682]
  3.7.83 \(\int \genfrac {}{}{}{}{\cos ^4(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [683]
  3.7.84 \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [684]
  3.7.85 \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [685]
  3.7.86 \(\int \genfrac {}{}{}{}{\sec (c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [686]
  3.7.87 \(\int \genfrac {}{}{}{}{A+C \sec ^2(c+d x)}{(a+b \sec (c+d x))^2} \, dx\) [687]
  3.7.88 \(\int \genfrac {}{}{}{}{\cos (c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [688]
  3.7.89 \(\int \genfrac {}{}{}{}{\cos ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [689]
  3.7.90 \(\int \genfrac {}{}{}{}{\cos ^3(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [690]
  3.7.91 \(\int \genfrac {}{}{}{}{\sec ^4(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [691]
  3.7.92 \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [692]
  3.7.93 \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [693]
  3.7.94 \(\int \genfrac {}{}{}{}{\sec (c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [694]
  3.7.95 \(\int \genfrac {}{}{}{}{A+C \sec ^2(c+d x)}{(a+b \sec (c+d x))^3} \, dx\) [695]
  3.7.96 \(\int \genfrac {}{}{}{}{\cos (c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [696]
  3.7.97 \(\int \genfrac {}{}{}{}{\cos ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [697]
  3.7.98 \(\int \genfrac {}{}{}{}{\sec ^4(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^4} \, dx\) [698]
  3.7.99 \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^4} \, dx\) [699]
  3.7.100 \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^4} \, dx\) [700]