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