Integral de dx/sin^25x dx

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 |                                                                                                     13                      9                     17                     5                    21                                       23                     3                     19                      7                      15                      11               
 |    1              676039*log(1 + cos(x))   676039*log(-1 + cos(x))                - 221803567050*cos  (x) - 197767334710*cos (x) - 67013911107*cos  (x) - 46038446685*cos (x) - 3904125225*cos  (x) - 1741541175*cos(x) + 334639305*cos  (x) + 12013258455*cos (x) + 20814564771*cos  (x) + 114444262845*cos (x) + 144986993866*cos  (x) + 245588699190*cos  (x)            
 | -------- dx = C - ---------------------- + ----------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 |    25                    8388608                   8388608                                         10                       14                      6                      18                     2                     22                    24                      4                      20                       8                       16                       12   
 | sin  (x)                                                             2076180480 - 1644334940160*cos  (x) - 1644334940160*cos  (x) - 456759705600*cos (x) - 456759705600*cos  (x) - 24914165760*cos (x) - 24914165760*cos  (x) + 2076180480*cos  (x) + 137027911680*cos (x) + 137027911680*cos  (x) + 1027709337600*cos (x) + 1027709337600*cos  (x) + 1918390763520*cos  (x)
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$$\int \frac{1}{\sin^{25}{\left(x \right)}}\, dx = C + \frac{334639305 \cos^{23}{\left(x \right)} - 3904125225 \cos^{21}{\left(x \right)} + 20814564771 \cos^{19}{\left(x \right)} - 67013911107 \cos^{17}{\left(x \right)} + 144986993866 \cos^{15}{\left(x \right)} - 221803567050 \cos^{13}{\left(x \right)} + 245588699190 \cos^{11}{\left(x \right)} - 197767334710 \cos^{9}{\left(x \right)} + 114444262845 \cos^{7}{\left(x \right)} - 46038446685 \cos^{5}{\left(x \right)} + 12013258455 \cos^{3}{\left(x \right)} - 1741541175 \cos{\left(x \right)}}{2076180480 \cos^{24}{\left(x \right)} - 24914165760 \cos^{22}{\left(x \right)} + 137027911680 \cos^{20}{\left(x \right)} - 456759705600 \cos^{18}{\left(x \right)} + 1027709337600 \cos^{16}{\left(x \right)} - 1644334940160 \cos^{14}{\left(x \right)} + 1918390763520 \cos^{12}{\left(x \right)} - 1644334940160 \cos^{10}{\left(x \right)} + 1027709337600 \cos^{8}{\left(x \right)} - 456759705600 \cos^{6}{\left(x \right)} + 137027911680 \cos^{4}{\left(x \right)} - 24914165760 \cos^{2}{\left(x \right)} + 2076180480} + \frac{676039 \log{\left(\cos{\left(x \right)} - 1 \right)}}{8388608} - \frac{676039 \log{\left(\cos{\left(x \right)} + 1 \right)}}{8388608}$$

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