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cos^52x/sin^82x

Integral of cos^52x/sin^82x dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |     52      
 |  cos  (x)   
 |  -------- dx
 |     82      
 |  sin  (x)   
 |             
/              
0              
$$\int\limits_{0}^{1} \frac{\cos^{52}{\left(x \right)}}{\sin^{82}{\left(x \right)}}\, dx$$
Integral(cos(x)^52/(sin(x)^82), (x, 0, 1))
The answer (Indefinite) [src]
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 | cos  (x)          160329014038666934208532*cos(x)   9561856572438900221401*cos(x)   1607517633411683617036*cos(x)   1602472061843966301781*cos(x)   5911889050192793122*cos(x)   4203551791790935423*cos(x)   8995106989847362*cos(x)    2373737631116927*cos(x)    2020954810886251*cos(x)    36017228877266*cos(x)   22308242918*cos(x)         33554432*cos(x)               16777216*cos(x)                 4194304*cos(x)                 2097152*cos(x)                 1835008*cos(x)                 917504*cos(x)                  229376*cos(x)                  212992*cos(x)                  113152*cos(x)                  99008*cos(x)           91507*cos(x)            28288*cos(x)                  13312*cos(x)                  12376*cos(x)                  476*cos(x)                 17*cos(x)              cos(x)      2026*cos(x)    54049268*cos(x)    760433375156*cos(x)     86342528635738*cos(x)      690862874725136*cos(x)   6750163959008912*cos(x)   41667137547699346*cos(x)   889716632321616028*cos(x)   23331419354498899508*cos(x)   56263396415875297532*cos(x)   1761688673648887859122*cos(x)   91722895980188070616984*cos(x)   366996649667573283524608*cos(x)
 | -------- dx = C - ------------------------------- - ----------------------------- - ----------------------------- - ----------------------------- - -------------------------- - -------------------------- - ------------------------ - ----------------------- - ------------------------- - --------------------- - ------------------ - --------------------------- - ---------------------------- - ---------------------------- - ---------------------------- - ---------------------------- - ---------------------------- - ---------------------------- - ---------------------------- - --------------------------- - --------------------------- - -------------- - --------------------------- - --------------------------- - --------------------------- - ------------------------- - ------------------------ - ----------- + ------------- + ---------------- + ------------------- + ------------------------- + ----------------------- + ----------------------- + ------------------------ + ------------------------- + --------------------------- + --------------------------- + ----------------------------- + ------------------------------ + -------------------------------
 |    82                                      53                              49                              57                              45                           41                          61                           37                       65                           33                      69                   73      50937774768799055775*sin(x)                           3                              5                              7                              9                             11                             13                             15                            19                            23               77                            21                            17                            25                          27                         29            81              79                 75                    71                          31                        35                       67                         63                           39                           59                             43                             47                              55                                 51    
 | sin  (x)            1886584250696261325*sin  (x)     226390110083551359*sin  (x)      17474365272315285*sin  (x)     147645723967533495*sin  (x)    4474112847501015*sin  (x)     77940969100425*sin  (x)     141287774131611*sin  (x)    141968978325*sin  (x)    2590275859079535*sin  (x)    13985003835*sin  (x)   128459925*sin  (x)                                 50937774768799055775*sin (x)   16979258256266351925*sin (x)   10187554953759811155*sin (x)   10187554953759811155*sin (x)   5659752752088783975*sin  (x)   1543568932387850175*sin  (x)   1543568932387850175*sin  (x)   926141359432710105*sin  (x)   893645171382439575*sin  (x)   23463*sin  (x)   243721410377028975*sin  (x)   102904595492523345*sin  (x)   116562413658579075*sin  (x)   4662496546343163*sin  (x)   172685057271969*sin  (x)   81*sin  (x)   6399*sin  (x)   1759725*sin  (x)   1013406075*sin  (x)   2590275859079535*sin  (x)   78493207850895*sin  (x)    936995256945*sin  (x)     1277720804925*sin  (x)    2684467708500609*sin  (x)     306567811795005*sin  (x)     13422338542503045*sin  (x)     75463370027850453*sin  (x)     961090089977340675*sin  (x)       5659752752088783975*sin  (x) 
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$$-{{961090089977340675\,\tan ^{28}x+12965979032057941470\,\tan ^{26} x+81321710595802001325\,\tan ^{24}x+314260169760048411900\,\tan ^{22 }x+835880533501112374275\,\tan ^{20}x+1618689287097392216850\,\tan ^{18}x+2353325194318516376805\,\tan ^{16}x+2609230492634602379400\, \tan ^{14}x+2216900545372515427425\,\tan ^{12}x+ 1436301761790643798050\,\tan ^{10}x+698475514295450066175\,\tan ^8x+ 247218000211238084028\,\tan ^6x+60199188363126156825\,\tan ^4x+ 9026947427382111150\,\tan ^2x+628861416898753775}\over{ 50937774768799055775\,\tan ^{81}x}}$$
The graph
The answer [src]
oo
$${\it \%a}$$
=
=
oo
$$\infty$$
Numerical answer [src]
5.76112492767049e+1538
5.76112492767049e+1538
The graph
Integral of cos^52x/sin^82x dx

    Use the examples entering the upper and lower limits of integration.