\(\int \genfrac {}{}{}{}{a+b \sin (d+e x)}{b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x)} \, dx\) [501]
   \(\int \genfrac {}{}{}{}{a+b \sin (d+e x)}{(b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x))^2} \, dx\) [502]
   \(\int \genfrac {}{}{}{}{d+e \sin (x)}{a+b \sin (x)+c \sin ^2(x)} \, dx\) [503]
   \(\int (a+b \sin (d+e x)) (b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x))^{3/2} \, dx\) [504]
   \(\int (a+b \sin (d+e x)) \sqrt {b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x)} \, dx\) [505]
   \(\int \genfrac {}{}{}{}{a+b \sin (d+e x)}{\sqrt {b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x)}} \, dx\) [506]
   \(\int \genfrac {}{}{}{}{a+b \sin (d+e x)}{(b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x))^{3/2}} \, dx\) [507]
   \(\int \genfrac {}{}{}{}{a+b \cos (x)}{b^2+2 a b \cos (x)+a^2 \cos ^2(x)} \, dx\) [508]
   \(\int \genfrac {}{}{}{}{d+e \cos (x)}{a+b \cos (x)+c \cos ^2(x)} \, dx\) [509]
   \(\int (a+b \tan (d+e x)) (b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x))^2 \, dx\) [510]
   \(\int (a+b \tan (d+e x)) (b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x)) \, dx\) [511]
   \(\int \genfrac {}{}{}{}{a+b \tan (d+e x)}{b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x)} \, dx\) [512]
   \(\int \genfrac {}{}{}{}{a+b \tan (d+e x)}{(b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x))^2} \, dx\) [513]
   \(\int (a+b \tan (d+e x)) (b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x))^{3/2} \, dx\) [514]
   \(\int (a+b \tan (d+e x)) \sqrt {b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x)} \, dx\) [515]
   \(\int \genfrac {}{}{}{}{a+b \tan (d+e x)}{\sqrt {b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x)}} \, dx\) [516]
   \(\int \genfrac {}{}{}{}{a+b \tan (d+e x)}{(b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x))^{3/2}} \, dx\) [517]
   \(\int (a+b \sec (d+e x)) (b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x))^2 \, dx\) [518]
   \(\int (a+b \sec (d+e x)) (b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x)) \, dx\) [519]
   \(\int \genfrac {}{}{}{}{a+b \sec (d+e x)}{b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x)} \, dx\) [520]
   \(\int \genfrac {}{}{}{}{a+b \sec (d+e x)}{(b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x))^2} \, dx\) [521]
   \(\int (a+b \sec (d+e x)) (b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x))^{3/2} \, dx\) [522]
   \(\int (a+b \sec (d+e x)) \sqrt {b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x)} \, dx\) [523]
   \(\int \genfrac {}{}{}{}{a+b \sec (d+e x)}{\sqrt {b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x)}} \, dx\) [524]
   \(\int \genfrac {}{}{}{}{a+b \sec (d+e x)}{(b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x))^{3/2}} \, dx\) [525]
   \(\int \genfrac {}{}{}{}{\cos (x)-i \sin (x)}{\cos (x)+i \sin (x)} \, dx\) [526]
   \(\int \genfrac {}{}{}{}{\cos (x)+i \sin (x)}{\cos (x)-i \sin (x)} \, dx\) [527]
   \(\int \genfrac {}{}{}{}{\cos (x)-\sin (x)}{\cos (x)+\sin (x)} \, dx\) [528]
   \(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{b \cos (x)+c \sin (x)} \, dx\) [529]
   \(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{(b \cos (x)+c \sin (x))^2} \, dx\) [530]
   \(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{(b \cos (x)+c \sin (x))^3} \, dx\) [531]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{b \cos (x)+c \sin (x)} \, dx\) [532]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{(b \cos (x)+c \sin (x))^2} \, dx\) [533]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{(b \cos (x)+c \sin (x))^3} \, dx\) [534]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)}{a+b \cos (x)+c \sin (x)} \, dx\) [535]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [536]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)}{(a+b \cos (x)+c \sin (x))^3} \, dx\) [537]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)}{a+b \cos (x)+i b \sin (x)} \, dx\) [538]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)}{a+b \cos (x)-i b \sin (x)} \, dx\) [539]
   \(\int \genfrac {}{}{}{}{A+C \sin (x)}{a+b \cos (x)+c \sin (x)} \, dx\) [540]
   \(\int \genfrac {}{}{}{}{A+C \sin (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [541]
   \(\int \genfrac {}{}{}{}{A+C \sin (x)}{(a+b \cos (x)+c \sin (x))^3} \, dx\) [542]
   \(\int \genfrac {}{}{}{}{A+C \sin (x)}{a+b \cos (x)+i b \sin (x)} \, dx\) [543]
   \(\int \genfrac {}{}{}{}{A+C \sin (x)}{a+b \cos (x)-i b \sin (x)} \, dx\) [544]
   \(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{a+b \cos (x)+c \sin (x)} \, dx\) [545]
   \(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [546]
   \(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{(a+b \cos (x)+c \sin (x))^3} \, dx\) [547]
   \(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{a+b \cos (x)+i b \sin (x)} \, dx\) [548]
   \(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{a+b \cos (x)-i b \sin (x)} \, dx\) [549]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{a+b \cos (x)+c \sin (x)} \, dx\) [550]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [551]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{(a+b \cos (x)+c \sin (x))^3} \, dx\) [552]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{a+b \cos (x)+i b \sin (x)} \, dx\) [553]
   \(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{a+b \cos (x)-i b \sin (x)} \, dx\) [554]
   \(\int \genfrac {}{}{}{}{b^2+c^2+a b \cos (x)+a c \sin (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [555]
   \(\int (a+b \cos (x)+c \sin (x))^{5/2} (d+b e \cos (x)+c e \sin (x)) \, dx\) [556]
   \(\int (a+b \cos (x)+c \sin (x))^{3/2} (d+b e \cos (x)+c e \sin (x)) \, dx\) [557]
   \(\int \sqrt {a+b \cos (x)+c \sin (x)} (d+b e \cos (x)+c e \sin (x)) \, dx\) [558]
   \(\int \genfrac {}{}{}{}{d+b e \cos (x)+c e \sin (x)}{\sqrt {a+b \cos (x)+c \sin (x)}} \, dx\) [559]
   \(\int \genfrac {}{}{}{}{d+b e \cos (x)+c e \sin (x)}{(a+b \cos (x)+c \sin (x))^{3/2}} \, dx\) [560]
   \(\int \genfrac {}{}{}{}{d+b e \cos (x)+c e \sin (x)}{(a+b \cos (x)+c \sin (x))^{5/2}} \, dx\) [561]
   \(\int \genfrac {}{}{}{}{A+B \cos (d+e x)+C \sin (d+e x)}{a+c \sin (d+e x)} \, dx\) [562]
   \(\int \genfrac {}{}{}{}{A+B \cos (d+e x)+C \sin (d+e x)}{(a+c \sin (d+e x))^2} \, dx\) [563]
   \(\int \genfrac {}{}{}{}{A+B \cos (d+e x)+C \sin (d+e x)}{(a+c \sin (d+e x))^3} \, dx\) [564]
   \(\int \genfrac {}{}{}{}{A+B \cos (d+e x)+C \sin (d+e x)}{(a+c \sin (d+e x))^4} \, dx\) [565]
   \(\int (a+b \cos (c+d x) \sin (c+d x))^m \, dx\) [566]
   \(\int (a+b \cos (c+d x) \sin (c+d x))^3 \, dx\) [567]
   \(\int (a+b \cos (c+d x) \sin (c+d x))^2 \, dx\) [568]
   \(\int (a+b \cos (c+d x) \sin (c+d x)) \, dx\) [569]
   \(\int \genfrac {}{}{}{}{1}{a+b \cos (c+d x) \sin (c+d x)} \, dx\) [570]
   \(\int \genfrac {}{}{}{}{1}{(a+b \cos (c+d x) \sin (c+d x))^2} \, dx\) [571]
   \(\int \genfrac {}{}{}{}{1}{(a+b \cos (c+d x) \sin (c+d x))^3} \, dx\) [572]
   \(\int (a+b \cos (c+d x) \sin (c+d x))^{5/2} \, dx\) [573]
   \(\int (a+b \cos (c+d x) \sin (c+d x))^{3/2} \, dx\) [574]
   \(\int \sqrt {a+b \cos (c+d x) \sin (c+d x)} \, dx\) [575]
   \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \cos (c+d x) \sin (c+d x)}} \, dx\) [576]
   \(\int \genfrac {}{}{}{}{1}{(a+b \cos (c+d x) \sin (c+d x))^{3/2}} \, dx\) [577]
   \(\int \genfrac {}{}{}{}{1}{(a+b \cos (c+d x) \sin (c+d x))^{5/2}} \, dx\) [578]
   \(\int \genfrac {}{}{}{}{x^3}{a+b \cos (x) \sin (x)} \, dx\) [579]
   \(\int \genfrac {}{}{}{}{x^2}{a+b \cos (x) \sin (x)} \, dx\) [580]
   \(\int \genfrac {}{}{}{}{x}{a+b \cos (x) \sin (x)} \, dx\) [581]
   \(\int \genfrac {}{}{}{}{1}{x (a+b \cos (x) \sin (x))} \, dx\) [582]
   \(\int \genfrac {}{}{}{}{(b x)^{2-n} \sin ^n(a x)}{(a c x \cos (a x)-c \sin (a x))^2} \, dx\) [583]
   \(\int \genfrac {}{}{}{}{(b x)^{2-n} \cos ^n(a x)}{(c \cos (a x)+a c x \sin (a x))^2} \, dx\) [584]
   \(\int \genfrac {}{}{}{}{\sin ^6(a x)}{x^4 (a x \cos (a x)-\sin (a x))^2} \, dx\) [585]
   \(\int \genfrac {}{}{}{}{\sin ^5(a x)}{x^3 (a x \cos (a x)-\sin (a x))^2} \, dx\) [586]
   \(\int \genfrac {}{}{}{}{\sin ^4(a x)}{x^2 (a x \cos (a x)-\sin (a x))^2} \, dx\) [587]
   \(\int \genfrac {}{}{}{}{\sin ^3(a x)}{x (a x \cos (a x)-\sin (a x))^2} \, dx\) [588]
   \(\int \genfrac {}{}{}{}{\sin ^2(a x)}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [589]
   \(\int \genfrac {}{}{}{}{x \sin (a x)}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [590]
   \(\int \genfrac {}{}{}{}{x^2}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [591]
   \(\int \genfrac {}{}{}{}{x^3 \csc (a x)}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [592]
   \(\int \genfrac {}{}{}{}{x^4 \csc ^2(a x)}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [593]
   \(\int \genfrac {}{}{}{}{\cos ^6(a x)}{x^4 (\cos (a x)+a x \sin (a x))^2} \, dx\) [594]
   \(\int \genfrac {}{}{}{}{\cos ^5(a x)}{x^3 (\cos (a x)+a x \sin (a x))^2} \, dx\) [595]
   \(\int \genfrac {}{}{}{}{\cos ^4(a x)}{x^2 (\cos (a x)+a x \sin (a x))^2} \, dx\) [596]
   \(\int \genfrac {}{}{}{}{\cos ^3(a x)}{x (\cos (a x)+a x \sin (a x))^2} \, dx\) [597]
   \(\int \genfrac {}{}{}{}{\cos ^2(a x)}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [598]
   \(\int \genfrac {}{}{}{}{x \cos (a x)}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [599]
   \(\int \genfrac {}{}{}{}{x^2}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [600]