Integral de 2cos2x\(sin²2x) dx

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 |                                                                21            3            19            17             9             7             13             11                                                                                                                                                                                           
 | 2*cos(2*x)                           15            5      2*cot  (x)   20*cot (x)   20*cot  (x)   90*cot  (x)   140*cot (x)   240*cot (x)   420*cot  (x)   504*cot  (x)     4*cos(x)      4*cos(x)       24*cos(x)       128*cos(x)       256*cos(x)      2048*cos(x)       3072*cos(x)      16384*cos(x)      32768*cos(x)     131072*cos(x)    262144*cos(x) 
 | ---------- dx = C + 2*cot(x) + 16*cot  (x) + 18*cot (x) + ---------- + ---------- + ----------- + ----------- + ----------- + ----------- + ------------ + ------------ - ----------- + ------------ + ------------- + -------------- + -------------- + -------------- + --------------- + -------------- + --------------- + --------------- + --------------
 |     22                                                        21           3             19            17            3             7             13             11              21             19              17               15               13                9                11                7                 5                 3      4849845*sin(x)
 |  sin  (x)                                                                                                                                                                 21*sin  (x)   399*sin  (x)   2261*sin  (x)   11305*sin  (x)   20995*sin  (x)   138567*sin (x)   230945*sin  (x)   969969*sin (x)   1616615*sin (x)   4849845*sin (x)                 
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$$\int \frac{2 \cos{\left(2 x \right)}}{\sin^{22}{\left(x \right)}}\, dx = C + \frac{2 \cot^{21}{\left(x \right)}}{21} + \frac{20 \cot^{19}{\left(x \right)}}{19} + \frac{90 \cot^{17}{\left(x \right)}}{17} + 16 \cot^{15}{\left(x \right)} + \frac{420 \cot^{13}{\left(x \right)}}{13} + \frac{504 \cot^{11}{\left(x \right)}}{11} + \frac{140 \cot^{9}{\left(x \right)}}{3} + \frac{240 \cot^{7}{\left(x \right)}}{7} + 18 \cot^{5}{\left(x \right)} + \frac{20 \cot^{3}{\left(x \right)}}{3} + 2 \cot{\left(x \right)} + \frac{262144 \cos{\left(x \right)}}{4849845 \sin{\left(x \right)}} + \frac{131072 \cos{\left(x \right)}}{4849845 \sin^{3}{\left(x \right)}} + \frac{32768 \cos{\left(x \right)}}{1616615 \sin^{5}{\left(x \right)}} + \frac{16384 \cos{\left(x \right)}}{969969 \sin^{7}{\left(x \right)}} + \frac{2048 \cos{\left(x \right)}}{138567 \sin^{9}{\left(x \right)}} + \frac{3072 \cos{\left(x \right)}}{230945 \sin^{11}{\left(x \right)}} + \frac{256 \cos{\left(x \right)}}{20995 \sin^{13}{\left(x \right)}} + \frac{128 \cos{\left(x \right)}}{11305 \sin^{15}{\left(x \right)}} + \frac{24 \cos{\left(x \right)}}{2261 \sin^{17}{\left(x \right)}} + \frac{4 \cos{\left(x \right)}}{399 \sin^{19}{\left(x \right)}} - \frac{4 \cos{\left(x \right)}}{21 \sin^{21}{\left(x \right)}}$$

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