\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^3 \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [1501]
   \(\int \sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1502]
   \(\int \sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1503]
   \(\int \sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1504]
   \(\int \sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1505]
   \(\int \sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1506]
   \(\int \sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1507]
   \(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1508]
   \(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1509]
   \(\int (a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1510]
   \(\int (a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1511]
   \(\int (a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1512]
   \(\int (a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1513]
   \(\int (a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1514]
   \(\int (a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1515]
   \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1516]
   \(\int (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{13}{2}}(c+d x) \, dx\) [1517]
   \(\int (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [1518]
   \(\int (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [1519]
   \(\int (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [1520]
   \(\int (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [1521]
   \(\int (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [1522]
   \(\int (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)} \, dx\) [1523]
   \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [1524]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x)}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1525]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1526]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1527]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1528]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1529]
   \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {a+b \cos (c+d x)} \sqrt {\sec (c+d x)}} \, dx\) [1530]
   \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {a+b \cos (c+d x)} \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1531]
   \(\int \genfrac {}{}{}{}{(a A+(A b+a B) \cos (c+d x)+b B \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{\sqrt {a+b \cos (c+d x)}} \, dx\) [1532]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1533]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1534]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1535]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{(a+b \cos (c+d x))^{3/2}} \, dx\) [1536]
   \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{3/2} \sqrt {\sec (c+d x)}} \, dx\) [1537]
   \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{3/2} \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [1538]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{(a+b \cos (c+d x))^{5/2}} \, dx\) [1539]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+b \cos (c+d x))^{5/2}} \, dx\) [1540]
   \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sqrt {\sec (c+d x)}}{(a+b \cos (c+d x))^{5/2}} \, dx\) [1541]