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3.6
Integrals 501 to 600
3.6.1
\(\int \genfrac {}{}{}{}{a+b \sin (d+e x)}{b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x)} \, dx\) [501]
3.6.2
\(\int \genfrac {}{}{}{}{a+b \sin (d+e x)}{(b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x))^2} \, dx\) [502]
3.6.3
\(\int \genfrac {}{}{}{}{d+e \sin (x)}{a+b \sin (x)+c \sin ^2(x)} \, dx\) [503]
3.6.4
\(\int (a+b \sin (d+e x)) (b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x))^{3/2} \, dx\) [504]
3.6.5
\(\int (a+b \sin (d+e x)) \sqrt {b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x)} \, dx\) [505]
3.6.6
\(\int \genfrac {}{}{}{}{a+b \sin (d+e x)}{\sqrt {b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x)}} \, dx\) [506]
3.6.7
\(\int \genfrac {}{}{}{}{a+b \sin (d+e x)}{(b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x))^{3/2}} \, dx\) [507]
3.6.8
\(\int \genfrac {}{}{}{}{a+b \cos (x)}{b^2+2 a b \cos (x)+a^2 \cos ^2(x)} \, dx\) [508]
3.6.9
\(\int \genfrac {}{}{}{}{d+e \cos (x)}{a+b \cos (x)+c \cos ^2(x)} \, dx\) [509]
3.6.10
\(\int (a+b \tan (d+e x)) (b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x))^2 \, dx\) [510]
3.6.11
\(\int (a+b \tan (d+e x)) (b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x)) \, dx\) [511]
3.6.12
\(\int \genfrac {}{}{}{}{a+b \tan (d+e x)}{b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x)} \, dx\) [512]
3.6.13
\(\int \genfrac {}{}{}{}{a+b \tan (d+e x)}{(b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x))^2} \, dx\) [513]
3.6.14
\(\int (a+b \tan (d+e x)) (b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x))^{3/2} \, dx\) [514]
3.6.15
\(\int (a+b \tan (d+e x)) \sqrt {b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x)} \, dx\) [515]
3.6.16
\(\int \genfrac {}{}{}{}{a+b \tan (d+e x)}{\sqrt {b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x)}} \, dx\) [516]
3.6.17
\(\int \genfrac {}{}{}{}{a+b \tan (d+e x)}{(b^2+2 a b \tan (d+e x)+a^2 \tan ^2(d+e x))^{3/2}} \, dx\) [517]
3.6.18
\(\int (a+b \sec (d+e x)) (b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x))^2 \, dx\) [518]
3.6.19
\(\int (a+b \sec (d+e x)) (b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x)) \, dx\) [519]
3.6.20
\(\int \genfrac {}{}{}{}{a+b \sec (d+e x)}{b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x)} \, dx\) [520]
3.6.21
\(\int \genfrac {}{}{}{}{a+b \sec (d+e x)}{(b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x))^2} \, dx\) [521]
3.6.22
\(\int (a+b \sec (d+e x)) (b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x))^{3/2} \, dx\) [522]
3.6.23
\(\int (a+b \sec (d+e x)) \sqrt {b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x)} \, dx\) [523]
3.6.24
\(\int \genfrac {}{}{}{}{a+b \sec (d+e x)}{\sqrt {b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x)}} \, dx\) [524]
3.6.25
\(\int \genfrac {}{}{}{}{a+b \sec (d+e x)}{(b^2+2 a b \sec (d+e x)+a^2 \sec ^2(d+e x))^{3/2}} \, dx\) [525]
3.6.26
\(\int \genfrac {}{}{}{}{\cos (x)-i \sin (x)}{\cos (x)+i \sin (x)} \, dx\) [526]
3.6.27
\(\int \genfrac {}{}{}{}{\cos (x)+i \sin (x)}{\cos (x)-i \sin (x)} \, dx\) [527]
3.6.28
\(\int \genfrac {}{}{}{}{\cos (x)-\sin (x)}{\cos (x)+\sin (x)} \, dx\) [528]
3.6.29
\(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{b \cos (x)+c \sin (x)} \, dx\) [529]
3.6.30
\(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{(b \cos (x)+c \sin (x))^2} \, dx\) [530]
3.6.31
\(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{(b \cos (x)+c \sin (x))^3} \, dx\) [531]
3.6.32
\(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{b \cos (x)+c \sin (x)} \, dx\) [532]
3.6.33
\(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{(b \cos (x)+c \sin (x))^2} \, dx\) [533]
3.6.34
\(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{(b \cos (x)+c \sin (x))^3} \, dx\) [534]
3.6.35
\(\int \genfrac {}{}{}{}{A+B \cos (x)}{a+b \cos (x)+c \sin (x)} \, dx\) [535]
3.6.36
\(\int \genfrac {}{}{}{}{A+B \cos (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [536]
3.6.37
\(\int \genfrac {}{}{}{}{A+B \cos (x)}{(a+b \cos (x)+c \sin (x))^3} \, dx\) [537]
3.6.38
\(\int \genfrac {}{}{}{}{A+B \cos (x)}{a+b \cos (x)+i b \sin (x)} \, dx\) [538]
3.6.39
\(\int \genfrac {}{}{}{}{A+B \cos (x)}{a+b \cos (x)-i b \sin (x)} \, dx\) [539]
3.6.40
\(\int \genfrac {}{}{}{}{A+C \sin (x)}{a+b \cos (x)+c \sin (x)} \, dx\) [540]
3.6.41
\(\int \genfrac {}{}{}{}{A+C \sin (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [541]
3.6.42
\(\int \genfrac {}{}{}{}{A+C \sin (x)}{(a+b \cos (x)+c \sin (x))^3} \, dx\) [542]
3.6.43
\(\int \genfrac {}{}{}{}{A+C \sin (x)}{a+b \cos (x)+i b \sin (x)} \, dx\) [543]
3.6.44
\(\int \genfrac {}{}{}{}{A+C \sin (x)}{a+b \cos (x)-i b \sin (x)} \, dx\) [544]
3.6.45
\(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{a+b \cos (x)+c \sin (x)} \, dx\) [545]
3.6.46
\(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [546]
3.6.47
\(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{(a+b \cos (x)+c \sin (x))^3} \, dx\) [547]
3.6.48
\(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{a+b \cos (x)+i b \sin (x)} \, dx\) [548]
3.6.49
\(\int \genfrac {}{}{}{}{B \cos (x)+C \sin (x)}{a+b \cos (x)-i b \sin (x)} \, dx\) [549]
3.6.50
\(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{a+b \cos (x)+c \sin (x)} \, dx\) [550]
3.6.51
\(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [551]
3.6.52
\(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{(a+b \cos (x)+c \sin (x))^3} \, dx\) [552]
3.6.53
\(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{a+b \cos (x)+i b \sin (x)} \, dx\) [553]
3.6.54
\(\int \genfrac {}{}{}{}{A+B \cos (x)+C \sin (x)}{a+b \cos (x)-i b \sin (x)} \, dx\) [554]
3.6.55
\(\int \genfrac {}{}{}{}{b^2+c^2+a b \cos (x)+a c \sin (x)}{(a+b \cos (x)+c \sin (x))^2} \, dx\) [555]
3.6.56
\(\int (a+b \cos (x)+c \sin (x))^{5/2} (d+b e \cos (x)+c e \sin (x)) \, dx\) [556]
3.6.57
\(\int (a+b \cos (x)+c \sin (x))^{3/2} (d+b e \cos (x)+c e \sin (x)) \, dx\) [557]
3.6.58
\(\int \sqrt {a+b \cos (x)+c \sin (x)} (d+b e \cos (x)+c e \sin (x)) \, dx\) [558]
3.6.59
\(\int \genfrac {}{}{}{}{d+b e \cos (x)+c e \sin (x)}{\sqrt {a+b \cos (x)+c \sin (x)}} \, dx\) [559]
3.6.60
\(\int \genfrac {}{}{}{}{d+b e \cos (x)+c e \sin (x)}{(a+b \cos (x)+c \sin (x))^{3/2}} \, dx\) [560]
3.6.61
\(\int \genfrac {}{}{}{}{d+b e \cos (x)+c e \sin (x)}{(a+b \cos (x)+c \sin (x))^{5/2}} \, dx\) [561]
3.6.62
\(\int \genfrac {}{}{}{}{A+B \cos (d+e x)+C \sin (d+e x)}{a+c \sin (d+e x)} \, dx\) [562]
3.6.63
\(\int \genfrac {}{}{}{}{A+B \cos (d+e x)+C \sin (d+e x)}{(a+c \sin (d+e x))^2} \, dx\) [563]
3.6.64
\(\int \genfrac {}{}{}{}{A+B \cos (d+e x)+C \sin (d+e x)}{(a+c \sin (d+e x))^3} \, dx\) [564]
3.6.65
\(\int \genfrac {}{}{}{}{A+B \cos (d+e x)+C \sin (d+e x)}{(a+c \sin (d+e x))^4} \, dx\) [565]
3.6.66
\(\int (a+b \cos (c+d x) \sin (c+d x))^m \, dx\) [566]
3.6.67
\(\int (a+b \cos (c+d x) \sin (c+d x))^3 \, dx\) [567]
3.6.68
\(\int (a+b \cos (c+d x) \sin (c+d x))^2 \, dx\) [568]
3.6.69
\(\int (a+b \cos (c+d x) \sin (c+d x)) \, dx\) [569]
3.6.70
\(\int \genfrac {}{}{}{}{1}{a+b \cos (c+d x) \sin (c+d x)} \, dx\) [570]
3.6.71
\(\int \genfrac {}{}{}{}{1}{(a+b \cos (c+d x) \sin (c+d x))^2} \, dx\) [571]
3.6.72
\(\int \genfrac {}{}{}{}{1}{(a+b \cos (c+d x) \sin (c+d x))^3} \, dx\) [572]
3.6.73
\(\int (a+b \cos (c+d x) \sin (c+d x))^{5/2} \, dx\) [573]
3.6.74
\(\int (a+b \cos (c+d x) \sin (c+d x))^{3/2} \, dx\) [574]
3.6.75
\(\int \sqrt {a+b \cos (c+d x) \sin (c+d x)} \, dx\) [575]
3.6.76
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \cos (c+d x) \sin (c+d x)}} \, dx\) [576]
3.6.77
\(\int \genfrac {}{}{}{}{1}{(a+b \cos (c+d x) \sin (c+d x))^{3/2}} \, dx\) [577]
3.6.78
\(\int \genfrac {}{}{}{}{1}{(a+b \cos (c+d x) \sin (c+d x))^{5/2}} \, dx\) [578]
3.6.79
\(\int \genfrac {}{}{}{}{x^3}{a+b \cos (x) \sin (x)} \, dx\) [579]
3.6.80
\(\int \genfrac {}{}{}{}{x^2}{a+b \cos (x) \sin (x)} \, dx\) [580]
3.6.81
\(\int \genfrac {}{}{}{}{x}{a+b \cos (x) \sin (x)} \, dx\) [581]
3.6.82
\(\int \genfrac {}{}{}{}{1}{x (a+b \cos (x) \sin (x))} \, dx\) [582]
3.6.83
\(\int \genfrac {}{}{}{}{(b x)^{2-n} \sin ^n(a x)}{(a c x \cos (a x)-c \sin (a x))^2} \, dx\) [583]
3.6.84
\(\int \genfrac {}{}{}{}{(b x)^{2-n} \cos ^n(a x)}{(c \cos (a x)+a c x \sin (a x))^2} \, dx\) [584]
3.6.85
\(\int \genfrac {}{}{}{}{\sin ^6(a x)}{x^4 (a x \cos (a x)-\sin (a x))^2} \, dx\) [585]
3.6.86
\(\int \genfrac {}{}{}{}{\sin ^5(a x)}{x^3 (a x \cos (a x)-\sin (a x))^2} \, dx\) [586]
3.6.87
\(\int \genfrac {}{}{}{}{\sin ^4(a x)}{x^2 (a x \cos (a x)-\sin (a x))^2} \, dx\) [587]
3.6.88
\(\int \genfrac {}{}{}{}{\sin ^3(a x)}{x (a x \cos (a x)-\sin (a x))^2} \, dx\) [588]
3.6.89
\(\int \genfrac {}{}{}{}{\sin ^2(a x)}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [589]
3.6.90
\(\int \genfrac {}{}{}{}{x \sin (a x)}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [590]
3.6.91
\(\int \genfrac {}{}{}{}{x^2}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [591]
3.6.92
\(\int \genfrac {}{}{}{}{x^3 \csc (a x)}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [592]
3.6.93
\(\int \genfrac {}{}{}{}{x^4 \csc ^2(a x)}{(a x \cos (a x)-\sin (a x))^2} \, dx\) [593]
3.6.94
\(\int \genfrac {}{}{}{}{\cos ^6(a x)}{x^4 (\cos (a x)+a x \sin (a x))^2} \, dx\) [594]
3.6.95
\(\int \genfrac {}{}{}{}{\cos ^5(a x)}{x^3 (\cos (a x)+a x \sin (a x))^2} \, dx\) [595]
3.6.96
\(\int \genfrac {}{}{}{}{\cos ^4(a x)}{x^2 (\cos (a x)+a x \sin (a x))^2} \, dx\) [596]
3.6.97
\(\int \genfrac {}{}{}{}{\cos ^3(a x)}{x (\cos (a x)+a x \sin (a x))^2} \, dx\) [597]
3.6.98
\(\int \genfrac {}{}{}{}{\cos ^2(a x)}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [598]
3.6.99
\(\int \genfrac {}{}{}{}{x \cos (a x)}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [599]
3.6.100
\(\int \genfrac {}{}{}{}{x^2}{(\cos (a x)+a x \sin (a x))^2} \, dx\) [600]
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