3.1.1 \(\int \sin ^3(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [1]
  3.1.2 \(\int \sin ^2(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [2]
  3.1.3 \(\int \sin (e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [3]
  3.1.4 \(\int (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [4]
  3.1.5 \(\int \csc (e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [5]
  3.1.6 \(\int \csc ^2(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [6]
  3.1.7 \(\int \csc ^3(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [7]
  3.1.8 \(\int \csc ^4(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [8]
  3.1.9 \(\int \csc ^5(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [9]
  3.1.10 \(\int \csc ^6(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [10]
  3.1.11 \(\int \csc ^7(e+f x) (a+a \sin (e+f x))^2 (c-c \sin (e+f x)) \, dx\) [11]
  3.1.12 \(\int \sin ^2(c+d x) (a+a \sin (c+d x))^{3/2} (c-c \sin (c+d x)) \, dx\) [12]
  3.1.13 \(\int \genfrac {}{}{}{}{\csc (e+f x) \sqrt {a+a \sin (e+f x)}}{c-c \sin (e+f x)} \, dx\) [13]
  3.1.14 \(\int \genfrac {}{}{}{}{\csc (e+f x)}{\sqrt {a+a \sin (e+f x)} (c-c \sin (e+f x))} \, dx\) [14]
  3.1.15 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)} \sqrt {a+a \sin (e+f x)}}{c-c \sin (e+f x)} \, dx\) [15]
  3.1.16 \(\int \genfrac {}{}{}{}{\sqrt {a+a \sin (e+f x)}}{\sqrt {g \sin (e+f x)} (c-c \sin (e+f x))} \, dx\) [16]
  3.1.17 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)}}{\sqrt {a+a \sin (e+f x)} (c-c \sin (e+f x))} \, dx\) [17]
  3.1.18 \(\int \genfrac {}{}{}{}{1}{\sqrt {g \sin (e+f x)} \sqrt {a+a \sin (e+f x)} (c-c \sin (e+f x))} \, dx\) [18]
  3.1.19 \(\int \csc (e+f x) \sqrt {a+a \sin (e+f x)} \sqrt {c-c \sin (e+f x)} \, dx\) [19]
  3.1.20 \(\int \genfrac {}{}{}{}{\csc (e+f x) \sqrt {a+a \sin (e+f x)}}{\sqrt {c-c \sin (e+f x)}} \, dx\) [20]
  3.1.21 \(\int \genfrac {}{}{}{}{\csc (e+f x) \sqrt {c-c \sin (e+f x)}}{\sqrt {a+a \sin (e+f x)}} \, dx\) [21]
  3.1.22 \(\int \genfrac {}{}{}{}{\csc (e+f x)}{\sqrt {a+a \sin (e+f x)} \sqrt {c-c \sin (e+f x)}} \, dx\) [22]
  3.1.23 \(\int \genfrac {}{}{}{}{\csc (e+f x) \sqrt {a+a \sin (e+f x)}}{c+d \sin (e+f x)} \, dx\) [23]
  3.1.24 \(\int \genfrac {}{}{}{}{\csc (e+f x)}{\sqrt {a+a \sin (e+f x)} (c+d \sin (e+f x))} \, dx\) [24]
  3.1.25 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)} \sqrt {a+a \sin (e+f x)}}{c+d \sin (e+f x)} \, dx\) [25]
  3.1.26 \(\int \genfrac {}{}{}{}{\sqrt {a+a \sin (e+f x)}}{\sqrt {g \sin (e+f x)} (c+d \sin (e+f x))} \, dx\) [26]
  3.1.27 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)}}{\sqrt {a+a \sin (e+f x)} (c+d \sin (e+f x))} \, dx\) [27]
  3.1.28 \(\int \genfrac {}{}{}{}{1}{\sqrt {g \sin (e+f x)} \sqrt {a+a \sin (e+f x)} (c+d \sin (e+f x))} \, dx\) [28]
  3.1.29 \(\int \genfrac {}{}{}{}{\csc (e+f x) \sqrt {a+b \sin (e+f x)}}{c+c \sin (e+f x)} \, dx\) [29]
  3.1.30 \(\int \genfrac {}{}{}{}{\csc (e+f x)}{\sqrt {a+b \sin (e+f x)} (c+c \sin (e+f x))} \, dx\) [30]
  3.1.31 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)} \sqrt {a+b \sin (e+f x)}}{c+c \sin (e+f x)} \, dx\) [31]
  3.1.32 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sin (e+f x)}}{\sqrt {g \sin (e+f x)} (c+c \sin (e+f x))} \, dx\) [32]
  3.1.33 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)}}{\sqrt {a+b \sin (e+f x)} (c+c \sin (e+f x))} \, dx\) [33]
  3.1.34 \(\int \genfrac {}{}{}{}{1}{\sqrt {g \sin (e+f x)} \sqrt {a+b \sin (e+f x)} (c+c \sin (e+f x))} \, dx\) [34]
  3.1.35 \(\int \csc (e+f x) \sqrt {a+a \sin (e+f x)} \sqrt {c+d \sin (e+f x)} \, dx\) [35]
  3.1.36 \(\int \genfrac {}{}{}{}{\csc (e+f x) \sqrt {a+a \sin (e+f x)}}{\sqrt {c+d \sin (e+f x)}} \, dx\) [36]
  3.1.37 \(\int \genfrac {}{}{}{}{\csc (e+f x) \sqrt {c+d \sin (e+f x)}}{\sqrt {a+a \sin (e+f x)}} \, dx\) [37]
  3.1.38 \(\int \genfrac {}{}{}{}{\csc (e+f x)}{\sqrt {a+a \sin (e+f x)} \sqrt {c+d \sin (e+f x)}} \, dx\) [38]
  3.1.39 \(\int \genfrac {}{}{}{}{\sin ^2(e+f x)}{(a+b \sin (e+f x))^2 (c+d \sin (e+f x))} \, dx\) [39]
  3.1.40 \(\int \genfrac {}{}{}{}{\csc (e+f x) \sqrt {c+d \sin (e+f x)}}{a+b \sin (e+f x)} \, dx\) [40]
  3.1.41 \(\int \genfrac {}{}{}{}{\csc (e+f x)}{(a+b \sin (e+f x)) \sqrt {c+d \sin (e+f x)}} \, dx\) [41]
  3.1.42 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)} \sqrt {a+b \sin (e+f x)}}{c+d \sin (e+f x)} \, dx\) [42]
  3.1.43 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sin (e+f x)}}{\sqrt {g \sin (e+f x)} (c+d \sin (e+f x))} \, dx\) [43]
  3.1.44 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)}}{\sqrt {a+b \sin (e+f x)} (c+d \sin (e+f x))} \, dx\) [44]
  3.1.45 \(\int \genfrac {}{}{}{}{1}{\sqrt {g \sin (e+f x)} \sqrt {a+b \sin (e+f x)} (c+d \sin (e+f x))} \, dx\) [45]
  3.1.46 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)} \sqrt {c+d \sin (e+f x)}}{a+b \sin (e+f x)} \, dx\) [46]
  3.1.47 \(\int \genfrac {}{}{}{}{\sqrt {g \sin (e+f x)}}{(a+b \sin (e+f x)) \sqrt {c+d \sin (e+f x)}} \, dx\) [47]
  3.1.48 \(\int \csc (e+f x) \sqrt {a+b \sin (e+f x)} \sqrt {c+d \sin (e+f x)} \, dx\) [48]
  3.1.49 \(\int \genfrac {}{}{}{}{\csc (e+f x) \sqrt {a+b \sin (e+f x)}}{\sqrt {c+d \sin (e+f x)}} \, dx\) [49]
  3.1.50 \(\int \genfrac {}{}{}{}{\csc (e+f x)}{\sqrt {a+b \sin (e+f x)} \sqrt {c+d \sin (e+f x)}} \, dx\) [50]
  3.1.51 \(\int (a+a \sin (e+f x))^m (A+B \sin (e+f x))^p (c-c \sin (e+f x))^n \, dx\) [51]