3.5.1 \(\int \genfrac {}{}{}{}{1}{(a+b \cos (d+e x)+c \sin (d+e x))^3} \, dx\) [401]
3.5.2 \(\int \genfrac {}{}{}{}{1}{(a+b \cos (d+e x)+c \sin (d+e x))^4} \, dx\) [402]
3.5.3 \(\int (2+3 \cos (d+e x)+5 \sin (d+e x))^{5/2} \, dx\) [403]
3.5.4 \(\int (2+3 \cos (d+e x)+5 \sin (d+e x))^{3/2} \, dx\) [404]
3.5.5 \(\int \sqrt {2+3 \cos (d+e x)+5 \sin (d+e x)} \, dx\) [405]
3.5.6 \(\int \genfrac {}{}{}{}{1}{\sqrt {2+3 \cos (d+e x)+5 \sin (d+e x)}} \, dx\) [406]
3.5.7 \(\int \genfrac {}{}{}{}{1}{(2+3 \cos (d+e x)+5 \sin (d+e x))^{3/2}} \, dx\) [407]
3.5.8 \(\int \genfrac {}{}{}{}{1}{(2+3 \cos (d+e x)+5 \sin (d+e x))^{5/2}} \, dx\) [408]
3.5.9 \(\int \genfrac {}{}{}{}{1}{(2+3 \cos (d+e x)+5 \sin (d+e x))^{7/2}} \, dx\) [409]
3.5.10 \(\int (a+b \cos (d+e x)+c \sin (d+e x))^{5/2} \, dx\) [410]
3.5.11 \(\int (a+b \cos (d+e x)+c \sin (d+e x))^{3/2} \, dx\) [411]
3.5.12 \(\int \sqrt {a+b \cos (d+e x)+c \sin (d+e x)} \, dx\) [412]
3.5.13 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \cos (d+e x)+c \sin (d+e x)}} \, dx\) [413]
3.5.14 \(\int \genfrac {}{}{}{}{1}{(a+b \cos (d+e x)+c \sin (d+e x))^{3/2}} \, dx\) [414]
3.5.15 \(\int \genfrac {}{}{}{}{1}{(a+b \cos (d+e x)+c \sin (d+e x))^{5/2}} \, dx\) [415]
3.5.16 \(\int \genfrac {}{}{}{}{1}{(a+b \cos (d+e x)+c \sin (d+e x))^{7/2}} \, dx\) [416]
3.5.17 \(\int (5+4 \cos (d+e x)+3 \sin (d+e x))^{5/2} \, dx\) [417]
3.5.18 \(\int (5+4 \cos (d+e x)+3 \sin (d+e x))^{3/2} \, dx\) [418]
3.5.19 \(\int \sqrt {5+4 \cos (d+e x)+3 \sin (d+e x)} \, dx\) [419]
3.5.20 \(\int \genfrac {}{}{}{}{1}{\sqrt {5+4 \cos (d+e x)+3 \sin (d+e x)}} \, dx\) [420]
3.5.21 \(\int \genfrac {}{}{}{}{1}{(5+4 \cos (d+e x)+3 \sin (d+e x))^{3/2}} \, dx\) [421]
3.5.22 \(\int \genfrac {}{}{}{}{1}{(5+4 \cos (d+e x)+3 \sin (d+e x))^{5/2}} \, dx\) [422]
3.5.23 \(\int (-5+4 \cos (d+e x)+3 \sin (d+e x))^{7/2} \, dx\) [423]
3.5.24 \(\int (-5+4 \cos (d+e x)+3 \sin (d+e x))^{5/2} \, dx\) [424]
3.5.25 \(\int (-5+4 \cos (d+e x)+3 \sin (d+e x))^{3/2} \, dx\) [425]
3.5.26 \(\int \sqrt {-5+4 \cos (d+e x)+3 \sin (d+e x)} \, dx\) [426]
3.5.27 \(\int \genfrac {}{}{}{}{1}{\sqrt {-5+4 \cos (d+e x)+3 \sin (d+e x)}} \, dx\) [427]
3.5.28 \(\int \genfrac {}{}{}{}{1}{(-5+4 \cos (d+e x)+3 \sin (d+e x))^{3/2}} \, dx\) [428]
3.5.29 \(\int \genfrac {}{}{}{}{1}{(-5+4 \cos (d+e x)+3 \sin (d+e x))^{5/2}} \, dx\) [429]
3.5.30 \(\int (\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x))^{7/2} \, dx\) [430]
3.5.31 \(\int (\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x))^{5/2} \, dx\) [431]
3.5.32 \(\int (\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x))^{3/2} \, dx\) [432]
3.5.33 \(\int \sqrt {\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x)} \, dx\) [433]
3.5.34 \(\int \genfrac {}{}{}{}{1}{\sqrt {\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x)}} \, dx\) [434]
3.5.35 \(\int \genfrac {}{}{}{}{1}{(\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x))^{3/2}} \, dx\) [435]
3.5.36 \(\int \genfrac {}{}{}{}{1}{(\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x))^{5/2}} \, dx\) [436]
3.5.37 \(\int (-\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x))^{5/2} \, dx\) [437]
3.5.38 \(\int (-\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x))^{3/2} \, dx\) [438]
3.5.39 \(\int \sqrt {-\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x)} \, dx\) [439]
3.5.40 \(\int \genfrac {}{}{}{}{1}{\sqrt {-\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x)}} \, dx\) [440]
3.5.41 \(\int \genfrac {}{}{}{}{1}{(-\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x))^{3/2}} \, dx\) [441]
3.5.42 \(\int \genfrac {}{}{}{}{1}{(-\sqrt {b^2+c^2}+b \cos (d+e x)+c \sin (d+e x))^{5/2}} \, dx\) [442]
3.5.43 \(\int \genfrac {}{}{}{}{\sin (x)}{a+b \cos (x)+c \sin (x)} \, dx\) [443]
3.5.44 \(\int \genfrac {}{}{}{}{\sin (x)}{1+\cos (x)+\sin (x)} \, dx\) [444]
3.5.45 \(\int \genfrac {}{}{}{}{1}{a+c \sec (x)+b \tan (x)} \, dx\) [445]
3.5.46 \(\int \genfrac {}{}{}{}{\sec (x)}{a+c \sec (x)+b \tan (x)} \, dx\) [446]
3.5.47 \(\int \genfrac {}{}{}{}{\sec ^2(x)}{a+c \sec (x)+b \tan (x)} \, dx\) [447]
3.5.48 \(\int \genfrac {}{}{}{}{(a+b \sec (d+e x)+c \tan (d+e x))^{3/2}}{\sec ^{\genfrac {}{}{}{}{3}{2}}(d+e x)} \, dx\) [448]
3.5.49 \(\int \genfrac {}{}{}{}{\sqrt {a+b \sec (d+e x)+c \tan (d+e x)}}{\sqrt {\sec (d+e x)}} \, dx\) [449]
3.5.50 \(\int \genfrac {}{}{}{}{\sqrt {\sec (d+e x)}}{\sqrt {a+b \sec (d+e x)+c \tan (d+e x)}} \, dx\) [450]
3.5.51 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{3}{2}}(d+e x)}{(a+b \sec (d+e x)+c \tan (d+e x))^{3/2}} \, dx\) [451]
3.5.52 \(\int \genfrac {}{}{}{}{\sec ^{\genfrac {}{}{}{}{5}{2}}(d+e x)}{(a+b \sec (d+e x)+c \tan (d+e x))^{5/2}} \, dx\) [452]
3.5.53 \(\int \cos ^{\genfrac {}{}{}{}{3}{2}}(d+e x) (a+b \sec (d+e x)+c \tan (d+e x))^{3/2} \, dx\) [453]
3.5.54 \(\int \sqrt {\cos (d+e x)} \sqrt {a+b \sec (d+e x)+c \tan (d+e x)} \, dx\) [454]
3.5.55 \(\int \genfrac {}{}{}{}{1}{\sqrt {\cos (d+e x)} \sqrt {a+b \sec (d+e x)+c \tan (d+e x)}} \, dx\) [455]
3.5.56 \(\int \genfrac {}{}{}{}{1}{\cos ^{\genfrac {}{}{}{}{3}{2}}(d+e x) (a+b \sec (d+e x)+c \tan (d+e x))^{3/2}} \, dx\) [456]
3.5.57 \(\int \genfrac {}{}{}{}{1}{\cos ^{\genfrac {}{}{}{}{5}{2}}(d+e x) (a+b \sec (d+e x)+c \tan (d+e x))^{5/2}} \, dx\) [457]
3.5.58 \(\int \genfrac {}{}{}{}{1}{a+b \cot (x)+c \csc (x)} \, dx\) [458]
3.5.59 \(\int \genfrac {}{}{}{}{\csc (x)}{a+b \cot (x)+c \csc (x)} \, dx\) [459]
3.5.60 \(\int \genfrac {}{}{}{}{\csc ^2(x)}{a+b \cot (x)+c \csc (x)} \, dx\) [460]
3.5.61 \(\int \genfrac {}{}{}{}{\csc (x)}{2+2 \cot (x)+3 \csc (x)} \, dx\) [461]
3.5.62 \(\int \genfrac {}{}{}{}{(a+c \cot (d+e x)+b \csc (d+e x))^{3/2}}{\csc ^{\genfrac {}{}{}{}{3}{2}}(d+e x)} \, dx\) [462]
3.5.63 \(\int \genfrac {}{}{}{}{\sqrt {a+c \cot (d+e x)+b \csc (d+e x)}}{\sqrt {\csc (d+e x)}} \, dx\) [463]
3.5.64 \(\int \genfrac {}{}{}{}{\sqrt {\csc (d+e x)}}{\sqrt {a+c \cot (d+e x)+b \csc (d+e x)}} \, dx\) [464]
3.5.65 \(\int \genfrac {}{}{}{}{\csc ^{\genfrac {}{}{}{}{3}{2}}(d+e x)}{(a+c \cot (d+e x)+b \csc (d+e x))^{3/2}} \, dx\) [465]
3.5.66 \(\int \genfrac {}{}{}{}{\csc ^{\genfrac {}{}{}{}{5}{2}}(d+e x)}{(a+c \cot (d+e x)+b \csc (d+e x))^{5/2}} \, dx\) [466]
3.5.67 \(\int (a+c \cot (d+e x)+b \csc (d+e x))^{3/2} \sin ^{\genfrac {}{}{}{}{3}{2}}(d+e x) \, dx\) [467]
3.5.68 \(\int \sqrt {a+c \cot (d+e x)+b \csc (d+e x)} \sqrt {\sin (d+e x)} \, dx\) [468]
3.5.69 \(\int \genfrac {}{}{}{}{1}{\sqrt {a+c \cot (d+e x)+b \csc (d+e x)} \sqrt {\sin (d+e x)}} \, dx\) [469]
3.5.70 \(\int \genfrac {}{}{}{}{1}{(a+c \cot (d+e x)+b \csc (d+e x))^{3/2} \sin ^{\genfrac {}{}{}{}{3}{2}}(d+e x)} \, dx\) [470]
3.5.71 \(\int \genfrac {}{}{}{}{1}{(a+c \cot (d+e x)+b \csc (d+e x))^{5/2} \sin ^{\genfrac {}{}{}{}{5}{2}}(d+e x)} \, dx\) [471]
3.5.72 \(\int \genfrac {}{}{}{}{1}{\cos ^2(x)+\sin ^2(x)} \, dx\) [472]
3.5.73 \(\int \genfrac {}{}{}{}{1}{(\cos ^2(x)+\sin ^2(x))^2} \, dx\) [473]
3.5.74 \(\int \genfrac {}{}{}{}{1}{(\cos ^2(x)+\sin ^2(x))^3} \, dx\) [474]
3.5.75 \(\int \genfrac {}{}{}{}{1}{\cos ^2(x)-\sin ^2(x)} \, dx\) [475]
3.5.76 \(\int \genfrac {}{}{}{}{1}{(\cos ^2(x)-\sin ^2(x))^2} \, dx\) [476]
3.5.77 \(\int \genfrac {}{}{}{}{1}{(\cos ^2(x)-\sin ^2(x))^3} \, dx\) [477]
3.5.78 \(\int \genfrac {}{}{}{}{1}{\cos ^2(x)+a^2 \sin ^2(x)} \, dx\) [478]
3.5.79 \(\int \genfrac {}{}{}{}{1}{b^2 \cos ^2(x)+\sin ^2(x)} \, dx\) [479]
3.5.80 \(\int \genfrac {}{}{}{}{1}{b^2 \cos ^2(x)+a^2 \sin ^2(x)} \, dx\) [480]
3.5.81 \(\int \genfrac {}{}{}{}{1}{4 \cos ^2(1+2 x)+3 \sin ^2(1+2 x)} \, dx\) [481]
3.5.82 \(\int \genfrac {}{}{}{}{\sin ^2(x)}{a \cos ^2(x)+b \sin ^2(x)} \, dx\) [482]
3.5.83 \(\int \genfrac {}{}{}{}{\cos ^2(x)}{a \cos ^2(x)+b \sin ^2(x)} \, dx\) [483]
3.5.84 \(\int \genfrac {}{}{}{}{1}{\sec ^2(x)+\tan ^2(x)} \, dx\) [484]
3.5.85 \(\int \genfrac {}{}{}{}{1}{(\sec ^2(x)+\tan ^2(x))^2} \, dx\) [485]
3.5.86 \(\int \genfrac {}{}{}{}{1}{(\sec ^2(x)+\tan ^2(x))^3} \, dx\) [486]
3.5.87 \(\int \genfrac {}{}{}{}{1}{\sec ^2(x)-\tan ^2(x)} \, dx\) [487]
3.5.88 \(\int \genfrac {}{}{}{}{1}{(\sec ^2(x)-\tan ^2(x))^2} \, dx\) [488]
3.5.89 \(\int \genfrac {}{}{}{}{1}{(\sec ^2(x)-\tan ^2(x))^3} \, dx\) [489]
3.5.90 \(\int \genfrac {}{}{}{}{1}{\cot ^2(x)+\csc ^2(x)} \, dx\) [490]
3.5.91 \(\int \genfrac {}{}{}{}{1}{(\cot ^2(x)+\csc ^2(x))^2} \, dx\) [491]
3.5.92 \(\int \genfrac {}{}{}{}{1}{(\cot ^2(x)+\csc ^2(x))^3} \, dx\) [492]
3.5.93 \(\int \genfrac {}{}{}{}{1}{\cot ^2(x)-\csc ^2(x)} \, dx\) [493]
3.5.94 \(\int \genfrac {}{}{}{}{1}{(\cot ^2(x)-\csc ^2(x))^2} \, dx\) [494]
3.5.95 \(\int \genfrac {}{}{}{}{1}{(\cot ^2(x)-\csc ^2(x))^3} \, dx\) [495]
3.5.96 \(\int \genfrac {}{}{}{}{1}{a+b \cos ^2(x)+c \sin ^2(x)} \, dx\) [496]
3.5.97 \(\int \genfrac {}{}{}{}{x}{a+b \cos ^2(x)+c \sin ^2(x)} \, dx\) [497]
3.5.98 \(\int \genfrac {}{}{}{}{x^2}{a+b \cos ^2(x)+c \sin ^2(x)} \, dx\) [498]
3.5.99 \(\int (a+b \sin (d+e x)) (b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x))^2 \, dx\) [499]
3.5.100 \(\int (a+b \sin (d+e x)) (b^2+2 a b \sin (d+e x)+a^2 \sin ^2(d+e x)) \, dx\) [500]