3.5.1 \(\int \genfrac {}{}{}{}{\sqrt {a+b \cos (c+d x)} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [401]
3.5.2 \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)) \, dx\) [402]
3.5.3 \(\int \sqrt {\cos (c+d x)} (a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x)) \, dx\) [403]
3.5.4 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [404]
3.5.5 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [405]
3.5.6 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [406]
3.5.7 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [407]
3.5.8 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [408]
3.5.9 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{3/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [409]
3.5.10 \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)) \, dx\) [410]
3.5.11 \(\int \sqrt {\cos (c+d x)} (a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x)) \, dx\) [411]
3.5.12 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [412]
3.5.13 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [413]
3.5.14 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [414]
3.5.15 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [415]
3.5.16 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [416]
3.5.17 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [417]
3.5.18 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (A+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{13}{2}}(c+d x)} \, dx\) [418]
3.5.19 \(\int \genfrac {}{}{}{}{(a+b \cos (c+d x))^{5/2} (\genfrac {}{}{}{}{3 b B}{2 a}+B \cos (c+d x))}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [419]
3.5.20 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x))}{\sqrt {a+b \cos (c+d x)}} \, dx\) [420]
3.5.21 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x))}{\sqrt {a+b \cos (c+d x)}} \, dx\) [421]
3.5.22 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\sqrt {\cos (c+d x)} \sqrt {a+b \cos (c+d x)}} \, dx\) [422]
3.5.23 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {a+b \cos (c+d x)}} \, dx\) [423]
3.5.24 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {a+b \cos (c+d x)}} \, dx\) [424]
3.5.25 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {a+b \cos (c+d x)}} \, dx\) [425]
3.5.26 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x))}{(a+b \cos (c+d x))^{3/2}} \, dx\) [426]
3.5.27 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x))}{(a+b \cos (c+d x))^{3/2}} \, dx\) [427]
3.5.28 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\sqrt {\cos (c+d x)} (a+b \cos (c+d x))^{3/2}} \, dx\) [428]
3.5.29 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \cos (c+d x))^{3/2}} \, dx\) [429]
3.5.30 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \cos (c+d x))^{3/2}} \, dx\) [430]
3.5.31 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \cos (c+d x))}{(a+b \cos (c+d x))^{5/2}} \, dx\) [431]
3.5.32 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x))}{(a+b \cos (c+d x))^{5/2}} \, dx\) [432]
3.5.33 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x))}{(a+b \cos (c+d x))^{5/2}} \, dx\) [433]
3.5.34 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\sqrt {\cos (c+d x)} (a+b \cos (c+d x))^{5/2}} \, dx\) [434]
3.5.35 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \cos (c+d x))^{5/2}} \, dx\) [435]
3.5.36 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (a+b \cos (c+d x))^{5/2}} \, dx\) [436]
3.5.37 \(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a B+b B \cos (c+d x))}{(a+b \cos (c+d x))^{3/2}} \, dx\) [437]
3.5.38 \(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (a B+b B \cos (c+d x))}{(a+b \cos (c+d x))^{3/2}} \, dx\) [438]
3.5.39 \(\int \genfrac {}{}{}{}{a B+b B \cos (c+d x)}{\sqrt {\cos (c+d x)} (a+b \cos (c+d x))^{3/2}} \, dx\) [439]
3.5.40 \(\int \genfrac {}{}{}{}{a B+b B \cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (a+b \cos (c+d x))^{3/2}} \, dx\) [440]
3.5.41 \(\int \genfrac {}{}{}{}{1+\cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {2+3 \cos (c+d x)}} \, dx\) [441]
3.5.42 \(\int \genfrac {}{}{}{}{1+\cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {-2+3 \cos (c+d x)}} \, dx\) [442]
3.5.43 \(\int \genfrac {}{}{}{}{1+\cos (c+d x)}{\sqrt {2-3 \cos (c+d x)} \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [443]
3.5.44 \(\int \genfrac {}{}{}{}{1+\cos (c+d x)}{\sqrt {-2-3 \cos (c+d x)} \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [444]
3.5.45 \(\int \genfrac {}{}{}{}{1+\cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {3+2 \cos (c+d x)}} \, dx\) [445]
3.5.46 \(\int \genfrac {}{}{}{}{1+\cos (c+d x)}{\sqrt {3-2 \cos (c+d x)} \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [446]
3.5.47 \(\int \genfrac {}{}{}{}{1+\cos (c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {-3+2 \cos (c+d x)}} \, dx\) [447]
3.5.48 \(\int \genfrac {}{}{}{}{1+\cos (c+d x)}{\sqrt {-3-2 \cos (c+d x)} \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [448]
3.5.49 \(\int (c \cos (e+f x))^m (a+b \cos (e+f x))^n (A+B \cos (e+f x)) \, dx\) [449]
3.5.50 \(\int (c \cos (e+f x))^m (a+b \cos (e+f x))^4 (A+B \cos (e+f x)) \, dx\) [450]
3.5.51 \(\int (c \cos (e+f x))^m (a+b \cos (e+f x))^3 (A+B \cos (e+f x)) \, dx\) [451]
3.5.52 \(\int (c \cos (e+f x))^m (a+b \cos (e+f x))^2 (A+B \cos (e+f x)) \, dx\) [452]
3.5.53 \(\int (c \cos (e+f x))^m (a+b \cos (e+f x)) (A+B \cos (e+f x)) \, dx\) [453]
3.5.54 \(\int \genfrac {}{}{}{}{(c \cos (e+f x))^m (A+B \cos (e+f x))}{a+b \cos (e+f x)} \, dx\) [454]
3.5.55 \(\int (c \cos (e+f x))^m (a+b \cos (e+f x))^{3/2} (A+B \cos (e+f x)) \, dx\) [455]
3.5.56 \(\int (c \cos (e+f x))^m \sqrt {a+b \cos (e+f x)} (A+B \cos (e+f x)) \, dx\) [456]
3.5.57 \(\int \genfrac {}{}{}{}{(c \cos (e+f x))^m (A+B \cos (e+f x))}{\sqrt {a+b \cos (e+f x)}} \, dx\) [457]
3.5.58 \(\int \genfrac {}{}{}{}{(c \cos (e+f x))^m (A+B \cos (e+f x))}{(a+b \cos (e+f x))^{3/2}} \, dx\) [458]
3.5.59 \(\int (a+a \cos (c+d x)) (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [459]
3.5.60 \(\int (a+a \cos (c+d x)) (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [460]
3.5.61 \(\int (a+a \cos (c+d x)) (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [461]
3.5.62 \(\int (a+a \cos (c+d x)) (A+B \cos (c+d x)) \sqrt {\sec (c+d x)} \, dx\) [462]
3.5.63 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x)) (A+B \cos (c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [463]
3.5.64 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x)) (A+B \cos (c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [464]
3.5.65 \(\int (a+a \cos (c+d x))^2 (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [465]
3.5.66 \(\int (a+a \cos (c+d x))^2 (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [466]
3.5.67 \(\int (a+a \cos (c+d x))^2 (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [467]
3.5.68 \(\int (a+a \cos (c+d x))^2 (A+B \cos (c+d x)) \sqrt {\sec (c+d x)} \, dx\) [468]
3.5.69 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x))^2 (A+B \cos (c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [469]
3.5.70 \(\int (a+a \cos (c+d x))^3 (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [470]
3.5.71 \(\int (a+a \cos (c+d x))^3 (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [471]
3.5.72 \(\int (a+a \cos (c+d x))^3 (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [472]
3.5.73 \(\int (a+a \cos (c+d x))^3 (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [473]
3.5.74 \(\int (a+a \cos (c+d x))^3 (A+B \cos (c+d x)) \sqrt {\sec (c+d x)} \, dx\) [474]
3.5.75 \(\int \genfrac {}{}{}{}{(a+a \cos (c+d x))^3 (A+B \cos (c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [475]
3.5.76 \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)}{a+a \cos (c+d x)} \, dx\) [476]
3.5.77 \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{a+a \cos (c+d x)} \, dx\) [477]
3.5.78 \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)) \sqrt {\sec (c+d x)}}{a+a \cos (c+d x)} \, dx\) [478]
3.5.79 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x)) \sqrt {\sec (c+d x)}} \, dx\) [479]
3.5.80 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [480]
3.5.81 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [481]
3.5.82 \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+a \cos (c+d x))^2} \, dx\) [482]
3.5.83 \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)) \sqrt {\sec (c+d x)}}{(a+a \cos (c+d x))^2} \, dx\) [483]
3.5.84 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x))^2 \sqrt {\sec (c+d x)}} \, dx\) [484]
3.5.85 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x))^2 \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [485]
3.5.86 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x))^2 \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [486]
3.5.87 \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)}{(a+a \cos (c+d x))^3} \, dx\) [487]
3.5.88 \(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)) \sqrt {\sec (c+d x)}}{(a+a \cos (c+d x))^3} \, dx\) [488]
3.5.89 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x))^3 \sqrt {\sec (c+d x)}} \, dx\) [489]
3.5.90 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x))^3 \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [490]
3.5.91 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x))^3 \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [491]
3.5.92 \(\int \genfrac {}{}{}{}{A+B \cos (c+d x)}{(a+a \cos (c+d x))^3 \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [492]
3.5.93 \(\int \sqrt {a+a \cos (c+d x)} (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{11}{2}}(c+d x) \, dx\) [493]
3.5.94 \(\int \sqrt {a+a \cos (c+d x)} (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \, dx\) [494]
3.5.95 \(\int \sqrt {a+a \cos (c+d x)} (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \, dx\) [495]
3.5.96 \(\int \sqrt {a+a \cos (c+d x)} (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \, dx\) [496]
3.5.97 \(\int \sqrt {a+a \cos (c+d x)} (A+B \cos (c+d x)) \sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \, dx\) [497]
3.5.98 \(\int \sqrt {a+a \cos (c+d x)} (A+B \cos (c+d x)) \sqrt {\sec (c+d x)} \, dx\) [498]
3.5.99 \(\int \genfrac {}{}{}{}{\sqrt {a+a \cos (c+d x)} (A+B \cos (c+d x))}{\sqrt {\sec (c+d x)}} \, dx\) [499]
3.5.100 \(\int \genfrac {}{}{}{}{\sqrt {a+a \cos (c+d x)} (A+B \cos (c+d x))}{\sec ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [500]