3.14 Integrals 1301 to 1373

   \(\int \cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^2 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1301]
   \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^2 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1302]
   \(\int \sqrt {\cos (c+d x)} (a+b \sec (c+d x))^2 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1303]
   \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^2 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1304]
   \(\int \cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x) (a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1305]
   \(\int \cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1306]
   \(\int \cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1307]
   \(\int \cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1308]
   \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1309]
   \(\int \sqrt {\cos (c+d x)} (a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1310]
   \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^3 (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1311]
   \(\int \cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x) (a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1312]
   \(\int \cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1313]
   \(\int \cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1314]
   \(\int \cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1315]
   \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1316]
   \(\int \sqrt {\cos (c+d x)} (a+b \sec (c+d x))^4 (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1317]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [1318]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [1319]
   \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{a+b \sec (c+d x)} \, dx\) [1320]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\cos (c+d x)} (a+b \sec (c+d x))} \, dx\) [1321]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))} \, dx\) [1322]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))} \, dx\) [1323]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [1324]
   \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^2} \, dx\) [1325]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\cos (c+d x)} (a+b \sec (c+d x))^2} \, dx\) [1326]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^2} \, dx\) [1327]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^2} \, dx\) [1328]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [1329]
   \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^3} \, dx\) [1330]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\cos (c+d x)} (a+b \sec (c+d x))^3} \, dx\) [1331]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^3} \, dx\) [1332]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^3} \, dx\) [1333]
   \(\int \cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1334]
   \(\int \cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1335]
   \(\int \cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1336]
   \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1337]
   \(\int \sqrt {\cos (c+d x)} \sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1338]
   \(\int \genfrac {}{}{}{}{\sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1339]
   \(\int \genfrac {}{}{}{}{\sqrt {a+b \sec (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1340]
   \(\int \cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1341]
   \(\int \cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1342]
   \(\int \cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1343]
   \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1344]
   \(\int \sqrt {\cos (c+d x)} (a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1345]
   \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1346]
   \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{3/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1347]
   \(\int \cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x) (a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1348]
   \(\int \cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1349]
   \(\int \cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1350]
   \(\int \cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1351]
   \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1352]
   \(\int \sqrt {\cos (c+d x)} (a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x)) \, dx\) [1353]
   \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [1354]
   \(\int \genfrac {}{}{}{}{(a+b \sec (c+d x))^{5/2} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1355]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+b \sec (c+d x)}} \, dx\) [1356]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+b \sec (c+d x)}} \, dx\) [1357]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+b \sec (c+d x)}} \, dx\) [1358]
   \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{\sqrt {a+b \sec (c+d x)}} \, dx\) [1359]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\cos (c+d x)} \sqrt {a+b \sec (c+d x)}} \, dx\) [1360]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+b \sec (c+d x)}} \, dx\) [1361]
   \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (a A+(A b+a B) \sec (c+d x)+b B \sec ^2(c+d x))}{\sqrt {a+b \sec (c+d x)}} \, dx\) [1362]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{3/2}} \, dx\) [1363]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{3/2}} \, dx\) [1364]
   \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{3/2}} \, dx\) [1365]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\cos (c+d x)} (a+b \sec (c+d x))^{3/2}} \, dx\) [1366]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^{3/2}} \, dx\) [1367]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{5/2}} \, dx\) [1368]
   \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{5/2}} \, dx\) [1369]
   \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \sec (c+d x)+C \sec ^2(c+d x))}{(a+b \sec (c+d x))^{5/2}} \, dx\) [1370]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\sqrt {\cos (c+d x)} (a+b \sec (c+d x))^{5/2}} \, dx\) [1371]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \sec (c+d x))^{5/2}} \, dx\) [1372]
   \(\int \genfrac {}{}{}{}{A+B \sec (c+d x)+C \sec ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \sec (c+d x))^{5/2}} \, dx\) [1373]