3.6.1 \(\int (a+b \sin ^2(e+f x))^{3/2} \tan (e+f x) \, dx\) [501]
  3.6.2 \(\int \cot (e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [502]
  3.6.3 \(\int \cot ^3(e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [503]
  3.6.4 \(\int \cot ^5(e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [504]
  3.6.5 \(\int (a+b \sin ^2(e+f x))^{3/2} \tan ^4(e+f x) \, dx\) [505]
  3.6.6 \(\int (a+b \sin ^2(e+f x))^{3/2} \tan ^2(e+f x) \, dx\) [506]
  3.6.7 \(\int (a+b \sin ^2(e+f x))^{3/2} \, dx\) [507]
  3.6.8 \(\int \cot ^2(e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [508]
  3.6.9 \(\int \cot ^4(e+f x) (a+b \sin ^2(e+f x))^{3/2} \, dx\) [509]
  3.6.10 \(\int \genfrac {}{}{}{}{\tan ^5(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [510]
  3.6.11 \(\int \genfrac {}{}{}{}{\tan ^3(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [511]
  3.6.12 \(\int \genfrac {}{}{}{}{\tan (e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [512]
  3.6.13 \(\int \genfrac {}{}{}{}{\cot (e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [513]
  3.6.14 \(\int \genfrac {}{}{}{}{\cot ^3(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [514]
  3.6.15 \(\int \genfrac {}{}{}{}{\cot ^5(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [515]
  3.6.16 \(\int \genfrac {}{}{}{}{\tan ^4(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [516]
  3.6.17 \(\int \genfrac {}{}{}{}{\tan ^2(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [517]
  3.6.18 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [518]
  3.6.19 \(\int \genfrac {}{}{}{}{\cot ^2(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [519]
  3.6.20 \(\int \genfrac {}{}{}{}{\cot ^4(e+f x)}{\sqrt {a+b \sin ^2(e+f x)}} \, dx\) [520]
  3.6.21 \(\int \genfrac {}{}{}{}{\tan ^5(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [521]
  3.6.22 \(\int \genfrac {}{}{}{}{\tan ^3(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [522]
  3.6.23 \(\int \genfrac {}{}{}{}{\tan (e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [523]
  3.6.24 \(\int \genfrac {}{}{}{}{\cot (e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [524]
  3.6.25 \(\int \genfrac {}{}{}{}{\cot ^3(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [525]
  3.6.26 \(\int \genfrac {}{}{}{}{\cot ^5(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [526]
  3.6.27 \(\int \genfrac {}{}{}{}{\tan ^4(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [527]
  3.6.28 \(\int \genfrac {}{}{}{}{\tan ^2(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [528]
  3.6.29 \(\int \genfrac {}{}{}{}{1}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [529]
  3.6.30 \(\int \genfrac {}{}{}{}{\cot ^2(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [530]
  3.6.31 \(\int \genfrac {}{}{}{}{\cot ^4(e+f x)}{(a+b \sin ^2(e+f x))^{3/2}} \, dx\) [531]
  3.6.32 \(\int \genfrac {}{}{}{}{\tan ^5(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [532]
  3.6.33 \(\int \genfrac {}{}{}{}{\tan ^3(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [533]
  3.6.34 \(\int \genfrac {}{}{}{}{\tan (e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [534]
  3.6.35 \(\int \genfrac {}{}{}{}{\cot (e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [535]
  3.6.36 \(\int \genfrac {}{}{}{}{\cot ^3(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [536]
  3.6.37 \(\int \genfrac {}{}{}{}{\cot ^5(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [537]
  3.6.38 \(\int \genfrac {}{}{}{}{\tan ^4(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [538]
  3.6.39 \(\int \genfrac {}{}{}{}{\tan ^2(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [539]
  3.6.40 \(\int \genfrac {}{}{}{}{1}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [540]
  3.6.41 \(\int \genfrac {}{}{}{}{\cot ^2(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [541]
  3.6.42 \(\int \genfrac {}{}{}{}{\cot ^4(e+f x)}{(a+b \sin ^2(e+f x))^{5/2}} \, dx\) [542]
  3.6.43 \(\int (a+b \sin ^2(e+f x))^p (d \tan (e+f x))^m \, dx\) [543]
  3.6.44 \(\int (a+b \sin ^2(c+d x))^p \tan ^3(c+d x) \, dx\) [544]
  3.6.45 \(\int (a+b \sin ^2(c+d x))^p \tan (c+d x) \, dx\) [545]
  3.6.46 \(\int \cot (c+d x) (a+b \sin ^2(c+d x))^p \, dx\) [546]
  3.6.47 \(\int \cot ^3(c+d x) (a+b \sin ^2(c+d x))^p \, dx\) [547]
  3.6.48 \(\int (a+b \sin ^2(c+d x))^p \tan ^4(c+d x) \, dx\) [548]
  3.6.49 \(\int (a+b \sin ^2(c+d x))^p \tan ^2(c+d x) \, dx\) [549]
  3.6.50 \(\int \cot ^2(c+d x) (a+b \sin ^2(c+d x))^p \, dx\) [550]
  3.6.51 \(\int \cot ^4(c+d x) (a+b \sin ^2(c+d x))^p \, dx\) [551]
  3.6.52 \(\int \genfrac {}{}{}{}{\cot ^3(x)}{a+b \sin ^3(x)} \, dx\) [552]
  3.6.53 \(\int \cot (x) \sqrt {a+b \sin ^3(x)} \, dx\) [553]
  3.6.54 \(\int \genfrac {}{}{}{}{\cot (x)}{\sqrt {a+b \sin ^3(x)}} \, dx\) [554]
  3.6.55 \(\int \cot (c+d x) \sqrt {a+b \sin ^4(c+d x)} \, dx\) [555]
  3.6.56 \(\int \genfrac {}{}{}{}{\tan ^3(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [556]
  3.6.57 \(\int \genfrac {}{}{}{}{\tan (c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [557]
  3.6.58 \(\int \genfrac {}{}{}{}{\cot (c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [558]
  3.6.59 \(\int \genfrac {}{}{}{}{\cot ^3(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [559]
  3.6.60 \(\int \genfrac {}{}{}{}{\cot ^5(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [560]
  3.6.61 \(\int \genfrac {}{}{}{}{\tan ^2(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [561]
  3.6.62 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [562]
  3.6.63 \(\int \genfrac {}{}{}{}{\cot ^2(c+d x)}{\sqrt {a+b \sin ^4(c+d x)}} \, dx\) [563]
  3.6.64 \(\int (a+b \sin ^4(c+d x))^p \tan ^m(c+d x) \, dx\) [564]
  3.6.65 \(\int (a+b \sin ^4(c+d x))^p \tan ^3(c+d x) \, dx\) [565]
  3.6.66 \(\int (a+b \sin ^4(c+d x))^p \tan (c+d x) \, dx\) [566]
  3.6.67 \(\int \cot (c+d x) (a+b \sin ^4(c+d x))^p \, dx\) [567]
  3.6.68 \(\int \cot ^3(c+d x) (a+b \sin ^4(c+d x))^p \, dx\) [568]
  3.6.69 \(\int (a+b \sin ^4(c+d x))^p \tan ^4(c+d x) \, dx\) [569]
  3.6.70 \(\int (a+b \sin ^4(c+d x))^p \tan ^2(c+d x) \, dx\) [570]
  3.6.71 \(\int (a+b \sin ^4(c+d x))^p \, dx\) [571]
  3.6.72 \(\int \cot ^2(c+d x) (a+b \sin ^4(c+d x))^p \, dx\) [572]
  3.6.73 \(\int \cot ^4(c+d x) (a+b \sin ^4(c+d x))^p \, dx\) [573]
  3.6.74 \(\int (a+b \sin ^n(c+d x))^3 \tan ^m(c+d x) \, dx\) [574]
  3.6.75 \(\int (a+b \sin ^n(c+d x))^2 \tan ^m(c+d x) \, dx\) [575]
  3.6.76 \(\int (a+b \sin ^n(c+d x)) \tan ^m(c+d x) \, dx\) [576]
  3.6.77 \(\int \genfrac {}{}{}{}{\tan ^m(c+d x)}{a+b \sin ^n(c+d x)} \, dx\) [577]
  3.6.78 \(\int \genfrac {}{}{}{}{\tan ^m(c+d x)}{(a+b \sin ^n(c+d x))^2} \, dx\) [578]
  3.6.79 \(\int \cot (x) \sqrt {a+b \sin ^n(x)} \, dx\) [579]
  3.6.80 \(\int \genfrac {}{}{}{}{\cot (x)}{\sqrt {a+b \sin ^n(x)}} \, dx\) [580]
  3.6.81 \(\int (a+b \sin ^n(c+d x))^p \tan ^m(c+d x) \, dx\) [581]
  3.6.82 \(\int (a+b \sin ^n(c+d x))^p \tan ^3(c+d x) \, dx\) [582]
  3.6.83 \(\int (a+b \sin ^n(c+d x))^p \tan (c+d x) \, dx\) [583]
  3.6.84 \(\int \cot (c+d x) (a+b \sin ^n(c+d x))^p \, dx\) [584]
  3.6.85 \(\int \cot ^3(c+d x) (a+b \sin ^n(c+d x))^p \, dx\) [585]
  3.6.86 \(\int (a+b \sin ^n(c+d x))^p \tan ^4(c+d x) \, dx\) [586]
  3.6.87 \(\int (a+b \sin ^n(c+d x))^p \tan ^2(c+d x) \, dx\) [587]
  3.6.88 \(\int (a+b \sin ^n(c+d x))^p \, dx\) [588]
  3.6.89 \(\int \cot ^2(c+d x) (a+b \sin ^n(c+d x))^p \, dx\) [589]
  3.6.90 \(\int \cot ^4(c+d x) (a+b \sin ^n(c+d x))^p \, dx\) [590]
  3.6.91 \(\int \genfrac {}{}{}{}{a+b \sin ^2(e+f x)}{(g \cos (e+f x))^{5/2} \sqrt {d \sin (e+f x)}} \, dx\) [591]
  3.6.92 \(\int (c \cos (e+f x))^m (d \sin (e+f x))^n (a+b \sin ^2(e+f x))^p \, dx\) [592]
  3.6.93 \(\int \sqrt {a+(c \cos (e+f x)+b \sin (e+f x))^2} \, dx\) [593]
  3.6.94 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+(c \cos (e+f x)+b \sin (e+f x))^2}} \, dx\) [594]