Интеграл cos(x)^(52) (dx)

Ответ

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 |                                     51                   49                    47                      45                       43                       41                         39                         37                          33                          35                          31                           29                            27                             21                             23                             17                             25                             9                             11                              13                              19                              15                              7                               3                               5                                         
 |     52          61989816618513   cos  (1)*sin(1)   51*cos  (1)*sin(1)   833*cos  (1)*sin(1)   39151*cos  (1)*sin(1)   352359*cos  (1)*sin(1)   721497*cos  (1)*sin(1)   29581377*cos  (1)*sin(1)   88744131*cos  (1)*sin(1)   150226993*cos  (1)*sin(1)   364836983*cos  (1)*sin(1)   450680979*cos  (1)*sin(1)   4657036783*cos  (1)*sin(1)   19293438101*cos  (1)*sin(1)   173640942909*cos  (1)*sin(1)   173640942909*cos  (1)*sin(1)   405162200121*cos  (1)*sin(1)   520922828727*cos  (1)*sin(1)   983965343151*cos (1)*sin(1)   983965343151*cos  (1)*sin(1)   2951896029453*cos  (1)*sin(1)   3646459801089*cos  (1)*sin(1)   6887757402057*cos  (1)*sin(1)   8855688088359*cos (1)*sin(1)   20663272206171*cos (1)*sin(1)   20663272206171*cos (1)*sin(1)   61989816618513*cos(1)*sin(1)
 |  cos  (x) dx = --------------- + --------------- + ------------------ + ------------------- + --------------------- + ---------------------- + ---------------------- + ------------------------ + ------------------------ + ------------------------- + ------------------------- + ------------------------- + -------------------------- + --------------------------- + ---------------------------- + ---------------------------- + ---------------------------- + ---------------------------- + --------------------------- + ---------------------------- + ----------------------------- + ----------------------------- + ----------------------------- + ---------------------------- + ----------------------------- + ----------------------------- + ----------------------------
 |                562949953421312          52                2600                 41600                 1913600                 16839680                 33679360                 1347174400                 3937894400                  6300631040                 15751577600                 18329108480                 183291084800                  733164339200                 5834713071616                  6099927302144                  12283606466560                 19062272819200                 21990232555520                24189255811072                  78615081385984                 116694261432320                 196537703464960                175921860444160                 281474976710656                 351843720888320                562949953421312       
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$${{6178807084575125\,\sin 32-1381051100\,\sin ^316+ 33332681717371665200\,\sin 16+101777941865600\,\sin ^58- 3684943083773952000\,\sin ^38+425412022998074112000\,\sin 8+ 984473600\,\sin ^{13}4-78748222259200\,\sin ^{11}4+67099200323584000 \,\sin ^94-6046407886268006400\,\sin ^74+114047465641318809600\, \sin ^54-659613407340029542400\,\sin ^34+1758965224541310156800\, \sin 4+218072401051648\,\sin ^{25}2-26547944475852800\,\sin ^{23}2+ 959518564627251200\,\sin ^{21}2-16160312667406336000\,\sin ^{19}2+ 153522970340360192000\,\sin ^{17}2-911089045801701212160\,\sin ^{15} 2+3585054529338055065600\,\sin ^{13}2-9684303144185914982400\,\sin ^{11}2+18276748580939104256000\,\sin ^92-24185772558235205632000\, \sin ^72+22250910753576389181440\,\sin ^52-14071722215700483276800\, \sin ^32+7035861107850241638400\,\sin 2+3099044504245996706400 }\over{28143444431400966553600}}$$

Численный ответ

0.172969862864835