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Identical expressions
- cos^52x/sin^82x
- co sinus of e of to the power of 52x divide by sinus of to the power of 82x
- cos52x/sin82x
- cos⁵2x/sin⁸2x
- cos^52x divide by sin^82x
- cos^52x/sin^82xdx
Integral of cos^52x/sin^82x dx
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]
/ | | 52 | 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) | /
$$-{{961090089977340675\,\tan ^{28}x+12965979032057941470\,\tan ^{26}
x+81321710595802001325\,\tan ^{24}x+314260169760048411900\,\tan ^{22
}x+835880533501112374275\,\tan ^{20}x+1618689287097392216850\,\tan
^{18}x+2353325194318516376805\,\tan ^{16}x+2609230492634602379400\,
\tan ^{14}x+2216900545372515427425\,\tan ^{12}x+
1436301761790643798050\,\tan ^{10}x+698475514295450066175\,\tan ^8x+
247218000211238084028\,\tan ^6x+60199188363126156825\,\tan ^4x+
9026947427382111150\,\tan ^2x+628861416898753775}\over{
50937774768799055775\,\tan ^{81}x}}$$
The graph
The graph
Use the examples entering the upper and lower limits of integration.