\(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [601]
   \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [602]
   \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [603]
   \(\int \genfrac {}{}{}{}{(a+a \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{13}{2}}(c+d x)} \, dx\) [604]
   \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+a \sec (c+d x)}} \, dx\) [605]
   \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+a \sec (c+d x)}} \, dx\) [606]
   \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+a \sec (c+d x)}} \, dx\) [607]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} \sqrt {a+a \sec (c+d x)}} \, dx\) [608]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \, dx\) [609]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \, dx\) [610]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {a+a \sec (c+d x)}} \, dx\) [611]
   \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (a A+(A b+a B) \sec (c+d x)+b B \sec ^2(c+d x))}{\sqrt {a+a \sec (c+d x)}} \, dx\) [612]
   \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx\) [613]
   \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx\) [614]
   \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{3/2}} \, dx\) [615]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{3/2}} \, dx\) [616]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx\) [617]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+a \sec (c+d x))^{3/2}} \, dx\) [618]
   \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{5/2}} \, dx\) [619]
   \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{5/2}} \, dx\) [620]
   \(\int \genfrac {}{}{}{}{\sqrt {\sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+a \sec (c+d x))^{5/2}} \, dx\) [621]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\sec (c+d x)} (a+a \sec (c+d x))^{5/2}} \, dx\) [622]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+a \sec (c+d x))^{5/2}} \, dx\) [623]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+a \sec (c+d x))^{5/2}} \, dx\) [624]
   \(\int (a+a \sec (c+d x))^{2/3} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [625]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt [3]{a+a \sec (c+d x)}} \, dx\) [626]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(a+a \sec (c+d x))^{4/3}} \, dx\) [627]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(a+a \sec (c+d x))^{7/3}} \, dx\) [628]
   \(\int (a+a \sec (c+d x))^{4/3} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [629]
   \(\int \sqrt [3]{a+a \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [630]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(a+a \sec (c+d x))^{2/3}} \, dx\) [631]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{(a+a \sec (c+d x))^{5/3}} \, dx\) [632]
   \(\int \sec ^m(c+d x) (a+a \sec (c+d x))^n (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [633]
   \(\int \sec ^{-1-n}(c+d x) (a+a \sec (c+d x))^n (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [634]
   \(\int (\genfrac {}{}{}{}{\sec ^{-n}(c+d x) (a+a \sec (c+d x))^n (-a (B+A n+B n)-a C (1+n) \sec (c+d x))}{a (1+n)}+\sec ^{-1-n}(c+d x) (a+a \sec (c+d x))^n (A+B \sec (c+d x)+C \sec ^2(c+d x))) \, dx\) [635]
   \(\int (a+a \sec (c+d x))^m (B-C+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [636]
   \(\int \sec ^3(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [637]
   \(\int \sec ^2(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [638]
   \(\int \sec (c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [639]
   \(\int (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [640]
   \(\int \cos (c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [641]
   \(\int \cos ^2(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [642]
   \(\int \cos ^3(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [643]
   \(\int \cos ^4(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [644]
   \(\int \cos ^5(c+d x) (a+b \sec (c+d x)) (A+C \sec ^2(c+d x)) \, dx\) [645]
   \(\int \sec ^2(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [646]
   \(\int \sec (c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [647]
   \(\int (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [648]
   \(\int \cos (c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [649]
   \(\int \cos ^2(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [650]
   \(\int \cos ^3(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [651]
   \(\int \cos ^4(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [652]
   \(\int \cos ^5(c+d x) (a+b \sec (c+d x))^2 (A+C \sec ^2(c+d x)) \, dx\) [653]
   \(\int \sec ^2(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [654]
   \(\int \sec (c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [655]
   \(\int (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [656]
   \(\int \cos (c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [657]
   \(\int \cos ^2(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [658]
   \(\int \cos ^3(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [659]
   \(\int \cos ^4(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [660]
   \(\int \cos ^5(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [661]
   \(\int \cos ^6(c+d x) (a+b \sec (c+d x))^3 (A+C \sec ^2(c+d x)) \, dx\) [662]
   \(\int \sec ^2(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [663]
   \(\int \sec (c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [664]
   \(\int (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [665]
   \(\int \cos (c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [666]
   \(\int \cos ^2(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [667]
   \(\int \cos ^3(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [668]
   \(\int \cos ^4(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [669]
   \(\int \cos ^5(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [670]
   \(\int \cos ^6(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [671]
   \(\int \cos ^7(c+d x) (a+b \sec (c+d x))^4 (A+C \sec ^2(c+d x)) \, dx\) [672]
   \(\int (a+b \sec (c+d x))^3 (a^2-b^2 \sec ^2(c+d x)) \, dx\) [673]
   \(\int (a+b \sec (c+d x))^2 (a^2-b^2 \sec ^2(c+d x)) \, dx\) [674]
   \(\int (a+b \sec (c+d x)) (a^2-b^2 \sec ^2(c+d x)) \, dx\) [675]
   \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [676]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [677]
   \(\int \genfrac {}{}{}{}{\sec (c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [678]
   \(\int \genfrac {}{}{}{}{A+C \sec ^2(c+d x)}{a+b \sec (c+d x)} \, dx\) [679]
   \(\int \genfrac {}{}{}{}{\cos (c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [680]
   \(\int \genfrac {}{}{}{}{\cos ^2(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [681]
   \(\int \genfrac {}{}{}{}{\cos ^3(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [682]
   \(\int \genfrac {}{}{}{}{\cos ^4(c+d x) (A+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [683]
   \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [684]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [685]
   \(\int \genfrac {}{}{}{}{\sec (c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [686]
   \(\int \genfrac {}{}{}{}{A+C \sec ^2(c+d x)}{(a+b \sec (c+d x))^2} \, dx\) [687]
   \(\int \genfrac {}{}{}{}{\cos (c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [688]
   \(\int \genfrac {}{}{}{}{\cos ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [689]
   \(\int \genfrac {}{}{}{}{\cos ^3(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [690]
   \(\int \genfrac {}{}{}{}{\sec ^4(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [691]
   \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [692]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [693]
   \(\int \genfrac {}{}{}{}{\sec (c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [694]
   \(\int \genfrac {}{}{}{}{A+C \sec ^2(c+d x)}{(a+b \sec (c+d x))^3} \, dx\) [695]
   \(\int \genfrac {}{}{}{}{\cos (c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [696]
   \(\int \genfrac {}{}{}{}{\cos ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [697]
   \(\int \genfrac {}{}{}{}{\sec ^4(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^4} \, dx\) [698]
   \(\int \genfrac {}{}{}{}{\sec ^3(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^4} \, dx\) [699]
   \(\int \genfrac {}{}{}{}{\sec ^2(c+d x) (A+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^4} \, dx\) [700]