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3.4
Integrals 301 to 393
3.4.1
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [301]
3.4.2
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [302]
3.4.3
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [303]
3.4.4
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [304]
3.4.5
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{3/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{13}{2}}(c+d x)} \, dx\) [305]
3.4.6
\(\int \sqrt {\cos (c+d x)} (b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [306]
3.4.7
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [307]
3.4.8
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [308]
3.4.9
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [309]
3.4.10
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [310]
3.4.11
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x)} \, dx\) [311]
3.4.12
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{11}{2}}(c+d x)} \, dx\) [312]
3.4.13
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{13}{2}}(c+d x)} \, dx\) [313]
3.4.14
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^{5/2} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{15}{2}}(c+d x)} \, dx\) [314]
3.4.15
\(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {b \cos (c+d x)}} \, dx\) [315]
3.4.16
\(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {b \cos (c+d x)}} \, dx\) [316]
3.4.17
\(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {b \cos (c+d x)}} \, dx\) [317]
3.4.18
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {\cos (c+d x)} \sqrt {b \cos (c+d x)}} \, dx\) [318]
3.4.19
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) \sqrt {b \cos (c+d x)}} \, dx\) [319]
3.4.20
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) \sqrt {b \cos (c+d x)}} \, dx\) [320]
3.4.21
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) \sqrt {b \cos (c+d x)}} \, dx\) [321]
3.4.22
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) \sqrt {b \cos (c+d x)}} \, dx\) [322]
3.4.23
\(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{3/2}} \, dx\) [323]
3.4.24
\(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{3/2}} \, dx\) [324]
3.4.25
\(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{3/2}} \, dx\) [325]
3.4.26
\(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{3/2}} \, dx\) [326]
3.4.27
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {\cos (c+d x)} (b \cos (c+d x))^{3/2}} \, dx\) [327]
3.4.28
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx\) [328]
3.4.29
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx\) [329]
3.4.30
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx\) [330]
3.4.31
\(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{9}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{5/2}} \, dx\) [331]
3.4.32
\(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{5/2}} \, dx\) [332]
3.4.33
\(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{5/2}} \, dx\) [333]
3.4.34
\(\int \genfrac {}{}{}{}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{5/2}} \, dx\) [334]
3.4.35
\(\int \genfrac {}{}{}{}{\sqrt {\cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{5/2}} \, dx\) [335]
3.4.36
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt {\cos (c+d x)} (b \cos (c+d x))^{5/2}} \, dx\) [336]
3.4.37
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx\) [337]
3.4.38
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx\) [338]
3.4.39
\(\int \cos (c+d x) (b \cos (c+d x))^{2/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [339]
3.4.40
\(\int (b \cos (c+d x))^{2/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [340]
3.4.41
\(\int (b \cos (c+d x))^{2/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec (c+d x) \, dx\) [341]
3.4.42
\(\int (b \cos (c+d x))^{2/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^2(c+d x) \, dx\) [342]
3.4.43
\(\int (b \cos (c+d x))^{2/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^3(c+d x) \, dx\) [343]
3.4.44
\(\int (b \cos (c+d x))^{2/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^4(c+d x) \, dx\) [344]
3.4.45
\(\int \cos (c+d x) (b \cos (c+d x))^{4/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [345]
3.4.46
\(\int (b \cos (c+d x))^{4/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [346]
3.4.47
\(\int (b \cos (c+d x))^{4/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec (c+d x) \, dx\) [347]
3.4.48
\(\int (b \cos (c+d x))^{4/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^2(c+d x) \, dx\) [348]
3.4.49
\(\int (b \cos (c+d x))^{4/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^3(c+d x) \, dx\) [349]
3.4.50
\(\int (b \cos (c+d x))^{4/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^4(c+d x) \, dx\) [350]
3.4.51
\(\int \genfrac {}{}{}{}{\cos ^2(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt [3]{b \cos (c+d x)}} \, dx\) [351]
3.4.52
\(\int \genfrac {}{}{}{}{\cos (c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt [3]{b \cos (c+d x)}} \, dx\) [352]
3.4.53
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt [3]{b \cos (c+d x)}} \, dx\) [353]
3.4.54
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec (c+d x)}{\sqrt [3]{b \cos (c+d x)}} \, dx\) [354]
3.4.55
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^2(c+d x)}{\sqrt [3]{b \cos (c+d x)}} \, dx\) [355]
3.4.56
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^3(c+d x)}{\sqrt [3]{b \cos (c+d x)}} \, dx\) [356]
3.4.57
\(\int \genfrac {}{}{}{}{\cos ^3(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{4/3}} \, dx\) [357]
3.4.58
\(\int \genfrac {}{}{}{}{\cos ^2(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{4/3}} \, dx\) [358]
3.4.59
\(\int \genfrac {}{}{}{}{\cos (c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{4/3}} \, dx\) [359]
3.4.60
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx\) [360]
3.4.61
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec (c+d x)}{(b \cos (c+d x))^{4/3}} \, dx\) [361]
3.4.62
\(\int \genfrac {}{}{}{}{(A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx\) [362]
3.4.63
\(\int \cos ^m(c+d x) (b \cos (c+d x))^{4/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [363]
3.4.64
\(\int \cos ^m(c+d x) (b \cos (c+d x))^{2/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [364]
3.4.65
\(\int \cos ^m(c+d x) \sqrt [3]{b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [365]
3.4.66
\(\int \genfrac {}{}{}{}{\cos ^m(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt [3]{b \cos (c+d x)}} \, dx\) [366]
3.4.67
\(\int \genfrac {}{}{}{}{\cos ^m(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{2/3}} \, dx\) [367]
3.4.68
\(\int \genfrac {}{}{}{}{\cos ^m(c+d x) (A+B \cos (c+d x)+C \cos ^2(c+d x))}{(b \cos (c+d x))^{4/3}} \, dx\) [368]
3.4.69
\(\int (a \cos (c+d x))^m (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [369]
3.4.70
\(\int \cos ^2(c+d x) (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [370]
3.4.71
\(\int \cos (c+d x) (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [371]
3.4.72
\(\int (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [372]
3.4.73
\(\int (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec (c+d x) \, dx\) [373]
3.4.74
\(\int (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^2(c+d x) \, dx\) [374]
3.4.75
\(\int (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^3(c+d x) \, dx\) [375]
3.4.76
\(\int (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \sec ^4(c+d x) \, dx\) [376]
3.4.77
\(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x) (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [377]
3.4.78
\(\int \sqrt {\cos (c+d x)} (b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [378]
3.4.79
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\sqrt {\cos (c+d x)}} \, dx\) [379]
3.4.80
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{3}{2}}(c+d x)} \, dx\) [380]
3.4.81
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{5}{2}}(c+d x)} \, dx\) [381]
3.4.82
\(\int \genfrac {}{}{}{}{(b \cos (c+d x))^n (A+B \cos (c+d x)+C \cos ^2(c+d x))}{\cos ^{\genfrac {}{}{}{}{7}{2}}(c+d x)} \, dx\) [382]
3.4.83
\(\int (a+a \cos (e+f x))^m (A+B \cos (e+f x)+C \cos ^2(e+f x)) \, dx\) [383]
3.4.84
\(\int (a+a \cos (c+d x))^{2/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [384]
3.4.85
\(\int \sqrt [3]{a+a \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [385]
3.4.86
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt [3]{a+a \cos (c+d x)}} \, dx\) [386]
3.4.87
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+a \cos (c+d x))^{2/3}} \, dx\) [387]
3.4.88
\(\int (a+b \cos (c+d x))^{2/3} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [388]
3.4.89
\(\int \sqrt [3]{a+b \cos (c+d x)} (A+B \cos (c+d x)+C \cos ^2(c+d x)) \, dx\) [389]
3.4.90
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{\sqrt [3]{a+b \cos (c+d x)}} \, dx\) [390]
3.4.91
\(\int \genfrac {}{}{}{}{A+B \cos (c+d x)+C \cos ^2(c+d x)}{(a+b \cos (c+d x))^{2/3}} \, dx\) [391]
3.4.92
\(\int (a+b \cos (e+f x))^m (A+(A+C) \cos (e+f x)+C \cos ^2(e+f x)) \, dx\) [392]
3.4.93
\(\int (a+b \cos (e+f x))^m (A+B \cos (e+f x)+C \cos ^2(e+f x)) \, dx\) [393]
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