3.3.1 \(\int \genfrac {}{}{}{}{1+\sin ^2(x)}{1-\sin ^2(x)} \, dx\) [201]
3.3.2 \(\int \genfrac {}{}{}{}{1-\sin ^2(x)}{1+\sin ^2(x)} \, dx\) [202]
3.3.3 \(\int \genfrac {}{}{}{}{1+\cos ^2(x)}{1-\cos ^2(x)} \, dx\) [203]
3.3.4 \(\int \genfrac {}{}{}{}{1-\cos ^2(x)}{1+\cos ^2(x)} \, dx\) [204]
3.3.5 \(\int \genfrac {}{}{}{}{-1+\genfrac {}{}{}{}{c^2}{d^2}+\sin ^2(x)}{c+d \cos (x)} \, dx\) [205]
3.3.6 \(\int \genfrac {}{}{}{}{a+b \sin ^2(x)}{c+d \cos (x)} \, dx\) [206]
3.3.7 \(\int \genfrac {}{}{}{}{a+b \sin ^2(x)}{c+c \cos ^2(x)} \, dx\) [207]
3.3.8 \(\int \genfrac {}{}{}{}{a+b \sin ^2(x)}{c-c \cos ^2(x)} \, dx\) [208]
3.3.9 \(\int \genfrac {}{}{}{}{a+b \sin ^2(x)}{c+d \cos ^2(x)} \, dx\) [209]
3.3.10 \(\int \genfrac {}{}{}{}{-1+\genfrac {}{}{}{}{c^2}{d^2}+\cos ^2(x)}{c+d \sin (x)} \, dx\) [210]
3.3.11 \(\int \genfrac {}{}{}{}{a+b \cos ^2(x)}{c+d \sin (x)} \, dx\) [211]
3.3.12 \(\int \genfrac {}{}{}{}{a+b \cos ^2(x)}{c+c \sin ^2(x)} \, dx\) [212]
3.3.13 \(\int \genfrac {}{}{}{}{a+b \cos ^2(x)}{c-c \sin ^2(x)} \, dx\) [213]
3.3.14 \(\int \genfrac {}{}{}{}{a+b \cos ^2(x)}{c+d \sin ^2(x)} \, dx\) [214]
3.3.15 \(\int \genfrac {}{}{}{}{a+b \sec ^2(x)}{c+d \cos (x)} \, dx\) [215]
3.3.16 \(\int \genfrac {}{}{}{}{a+b \csc ^2(x)}{c+d \sin (x)} \, dx\) [216]
3.3.17 \(\int (a \cos (c+d x)+b \sin (c+d x))^n \, dx\) [217]
3.3.18 \(\int (2 \cos (c+d x)+3 \sin (c+d x))^n \, dx\) [218]
3.3.19 \(\int (a \cos (c+d x)+b \sin (c+d x))^7 \, dx\) [219]
3.3.20 \(\int (a \cos (c+d x)+b \sin (c+d x))^6 \, dx\) [220]
3.3.21 \(\int (a \cos (c+d x)+b \sin (c+d x))^5 \, dx\) [221]
3.3.22 \(\int (a \cos (c+d x)+b \sin (c+d x))^4 \, dx\) [222]
3.3.23 \(\int (a \cos (c+d x)+b \sin (c+d x))^3 \, dx\) [223]
3.3.24 \(\int (a \cos (c+d x)+b \sin (c+d x))^2 \, dx\) [224]
3.3.25 \(\int (a \cos (c+d x)+b \sin (c+d x)) \, dx\) [225]
3.3.26 \(\int \genfrac {}{}{}{}{1}{a \cos (c+d x)+b \sin (c+d x)} \, dx\) [226]
3.3.27 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+b \sin (c+d x))^2} \, dx\) [227]
3.3.28 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+b \sin (c+d x))^3} \, dx\) [228]
3.3.29 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+b \sin (c+d x))^4} \, dx\) [229]
3.3.30 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+b \sin (c+d x))^5} \, dx\) [230]
3.3.31 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+b \sin (c+d x))^6} \, dx\) [231]
3.3.32 \(\int (a \cos (c+d x)+b \sin (c+d x))^{7/2} \, dx\) [232]
3.3.33 \(\int (a \cos (c+d x)+b \sin (c+d x))^{5/2} \, dx\) [233]
3.3.34 \(\int (a \cos (c+d x)+b \sin (c+d x))^{3/2} \, dx\) [234]
3.3.35 \(\int \sqrt {a \cos (c+d x)+b \sin (c+d x)} \, dx\) [235]
3.3.36 \(\int \genfrac {}{}{}{}{1}{\sqrt {a \cos (c+d x)+b \sin (c+d x)}} \, dx\) [236]
3.3.37 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+b \sin (c+d x))^{3/2}} \, dx\) [237]
3.3.38 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+b \sin (c+d x))^{5/2}} \, dx\) [238]
3.3.39 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+b \sin (c+d x))^{7/2}} \, dx\) [239]
3.3.40 \(\int (2 \cos (c+d x)+3 \sin (c+d x))^{7/2} \, dx\) [240]
3.3.41 \(\int (2 \cos (c+d x)+3 \sin (c+d x))^{5/2} \, dx\) [241]
3.3.42 \(\int (2 \cos (c+d x)+3 \sin (c+d x))^{3/2} \, dx\) [242]
3.3.43 \(\int \sqrt {2 \cos (c+d x)+3 \sin (c+d x)} \, dx\) [243]
3.3.44 \(\int \genfrac {}{}{}{}{1}{\sqrt {2 \cos (c+d x)+3 \sin (c+d x)}} \, dx\) [244]
3.3.45 \(\int \genfrac {}{}{}{}{1}{(2 \cos (c+d x)+3 \sin (c+d x))^{3/2}} \, dx\) [245]
3.3.46 \(\int \genfrac {}{}{}{}{1}{(2 \cos (c+d x)+3 \sin (c+d x))^{5/2}} \, dx\) [246]
3.3.47 \(\int \genfrac {}{}{}{}{1}{(2 \cos (c+d x)+3 \sin (c+d x))^{7/2}} \, dx\) [247]
3.3.48 \(\int (a \cos (c+d x)+i a \sin (c+d x))^n \, dx\) [248]
3.3.49 \(\int (a \cos (c+d x)+i a \sin (c+d x))^4 \, dx\) [249]
3.3.50 \(\int (a \cos (c+d x)+i a \sin (c+d x))^3 \, dx\) [250]
3.3.51 \(\int (a \cos (c+d x)+i a \sin (c+d x))^2 \, dx\) [251]
3.3.52 \(\int (a \cos (c+d x)+i a \sin (c+d x)) \, dx\) [252]
3.3.53 \(\int \genfrac {}{}{}{}{1}{a \cos (c+d x)+i a \sin (c+d x)} \, dx\) [253]
3.3.54 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+i a \sin (c+d x))^2} \, dx\) [254]
3.3.55 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+i a \sin (c+d x))^3} \, dx\) [255]
3.3.56 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+i a \sin (c+d x))^4} \, dx\) [256]
3.3.57 \(\int (a \cos (c+d x)+i a \sin (c+d x))^{5/2} \, dx\) [257]
3.3.58 \(\int (a \cos (c+d x)+i a \sin (c+d x))^{3/2} \, dx\) [258]
3.3.59 \(\int \sqrt {a \cos (c+d x)+i a \sin (c+d x)} \, dx\) [259]
3.3.60 \(\int \genfrac {}{}{}{}{1}{\sqrt {a \cos (c+d x)+i a \sin (c+d x)}} \, dx\) [260]
3.3.61 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+i a \sin (c+d x))^{3/2}} \, dx\) [261]
3.3.62 \(\int \genfrac {}{}{}{}{1}{(a \cos (c+d x)+i a \sin (c+d x))^{5/2}} \, dx\) [262]
3.3.63 \(\int (a \sec (x)+b \tan (x))^5 \, dx\) [263]
3.3.64 \(\int (a \sec (x)+b \tan (x))^4 \, dx\) [264]
3.3.65 \(\int (a \sec (x)+b \tan (x))^3 \, dx\) [265]
3.3.66 \(\int (a \sec (x)+b \tan (x))^2 \, dx\) [266]
3.3.67 \(\int (a \sec (x)+b \tan (x)) \, dx\) [267]
3.3.68 \(\int \genfrac {}{}{}{}{1}{a \sec (x)+b \tan (x)} \, dx\) [268]
3.3.69 \(\int \genfrac {}{}{}{}{1}{(a \sec (x)+b \tan (x))^2} \, dx\) [269]
3.3.70 \(\int \genfrac {}{}{}{}{1}{(a \sec (x)+b \tan (x))^3} \, dx\) [270]
3.3.71 \(\int \genfrac {}{}{}{}{1}{(a \sec (x)+b \tan (x))^4} \, dx\) [271]
3.3.72 \(\int \genfrac {}{}{}{}{1}{(a \sec (x)+b \tan (x))^5} \, dx\) [272]
3.3.73 \(\int (\sec (x)+\tan (x))^5 \, dx\) [273]
3.3.74 \(\int (\sec (x)+\tan (x))^4 \, dx\) [274]
3.3.75 \(\int (\sec (x)+\tan (x))^3 \, dx\) [275]
3.3.76 \(\int (\sec (x)+\tan (x))^2 \, dx\) [276]
3.3.77 \(\int (\sec (x)+\tan (x)) \, dx\) [277]
3.3.78 \(\int \genfrac {}{}{}{}{1}{\sec (x)+\tan (x)} \, dx\) [278]
3.3.79 \(\int \genfrac {}{}{}{}{1}{(\sec (x)+\tan (x))^2} \, dx\) [279]
3.3.80 \(\int \genfrac {}{}{}{}{1}{(\sec (x)+\tan (x))^3} \, dx\) [280]
3.3.81 \(\int \genfrac {}{}{}{}{1}{(\sec (x)+\tan (x))^4} \, dx\) [281]
3.3.82 \(\int \genfrac {}{}{}{}{1}{(\sec (x)+\tan (x))^5} \, dx\) [282]
3.3.83 \(\int (a \cot (x)+b \csc (x))^5 \, dx\) [283]
3.3.84 \(\int (a \cot (x)+b \csc (x))^4 \, dx\) [284]
3.3.85 \(\int (a \cot (x)+b \csc (x))^3 \, dx\) [285]
3.3.86 \(\int (a \cot (x)+b \csc (x))^2 \, dx\) [286]
3.3.87 \(\int (a \cot (x)+b \csc (x)) \, dx\) [287]
3.3.88 \(\int \genfrac {}{}{}{}{1}{a \cot (x)+b \csc (x)} \, dx\) [288]
3.3.89 \(\int \genfrac {}{}{}{}{1}{(a \cot (x)+b \csc (x))^2} \, dx\) [289]
3.3.90 \(\int \genfrac {}{}{}{}{1}{(a \cot (x)+b \csc (x))^3} \, dx\) [290]
3.3.91 \(\int \genfrac {}{}{}{}{1}{(a \cot (x)+b \csc (x))^4} \, dx\) [291]
3.3.92 \(\int \genfrac {}{}{}{}{1}{(a \cot (x)+b \csc (x))^5} \, dx\) [292]
3.3.93 \(\int (\cot (x)+\csc (x))^5 \, dx\) [293]
3.3.94 \(\int (\cot (x)+\csc (x))^4 \, dx\) [294]
3.3.95 \(\int (\cot (x)+\csc (x))^3 \, dx\) [295]
3.3.96 \(\int (\cot (x)+\csc (x))^2 \, dx\) [296]
3.3.97 \(\int (\cot (x)+\csc (x)) \, dx\) [297]
3.3.98 \(\int \genfrac {}{}{}{}{1}{\cot (x)+\csc (x)} \, dx\) [298]
3.3.99 \(\int \genfrac {}{}{}{}{1}{(\cot (x)+\csc (x))^2} \, dx\) [299]
3.3.100 \(\int \genfrac {}{}{}{}{1}{(\cot (x)+\csc (x))^3} \, dx\) [300]