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Integral de cos^52x/sin^82x dx
Solución
Ha introducido
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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))
Respuesta (Indefinida)
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/ | | 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) | /
$$\int \frac{\cos^{52}{\left(x \right)}}{\sin^{82}{\left(x \right)}}\, dx = C - \frac{33554432 \cos{\left(x \right)}}{50937774768799055775 \sin{\left(x \right)}} - \frac{16777216 \cos{\left(x \right)}}{50937774768799055775 \sin^{3}{\left(x \right)}} - \frac{4194304 \cos{\left(x \right)}}{16979258256266351925 \sin^{5}{\left(x \right)}} - \frac{2097152 \cos{\left(x \right)}}{10187554953759811155 \sin^{7}{\left(x \right)}} - \frac{1835008 \cos{\left(x \right)}}{10187554953759811155 \sin^{9}{\left(x \right)}} - \frac{917504 \cos{\left(x \right)}}{5659752752088783975 \sin^{11}{\left(x \right)}} - \frac{229376 \cos{\left(x \right)}}{1543568932387850175 \sin^{13}{\left(x \right)}} - \frac{212992 \cos{\left(x \right)}}{1543568932387850175 \sin^{15}{\left(x \right)}} - \frac{13312 \cos{\left(x \right)}}{102904595492523345 \sin^{17}{\left(x \right)}} - \frac{113152 \cos{\left(x \right)}}{926141359432710105 \sin^{19}{\left(x \right)}} - \frac{28288 \cos{\left(x \right)}}{243721410377028975 \sin^{21}{\left(x \right)}} - \frac{99008 \cos{\left(x \right)}}{893645171382439575 \sin^{23}{\left(x \right)}} - \frac{12376 \cos{\left(x \right)}}{116562413658579075 \sin^{25}{\left(x \right)}} - \frac{476 \cos{\left(x \right)}}{4662496546343163 \sin^{27}{\left(x \right)}} - \frac{17 \cos{\left(x \right)}}{172685057271969 \sin^{29}{\left(x \right)}} + \frac{86342528635738 \cos{\left(x \right)}}{2590275859079535 \sin^{31}{\left(x \right)}} - \frac{2020954810886251 \cos{\left(x \right)}}{2590275859079535 \sin^{33}{\left(x \right)}} + \frac{690862874725136 \cos{\left(x \right)}}{78493207850895 \sin^{35}{\left(x \right)}} - \frac{8995106989847362 \cos{\left(x \right)}}{141287774131611 \sin^{37}{\left(x \right)}} + \frac{889716632321616028 \cos{\left(x \right)}}{2684467708500609 \sin^{39}{\left(x \right)}} - \frac{5911889050192793122 \cos{\left(x \right)}}{4474112847501015 \sin^{41}{\left(x \right)}} + \frac{56263396415875297532 \cos{\left(x \right)}}{13422338542503045 \sin^{43}{\left(x \right)}} - \frac{1602472061843966301781 \cos{\left(x \right)}}{147645723967533495 \sin^{45}{\left(x \right)}} + \frac{1761688673648887859122 \cos{\left(x \right)}}{75463370027850453 \sin^{47}{\left(x \right)}} - \frac{9561856572438900221401 \cos{\left(x \right)}}{226390110083551359 \sin^{49}{\left(x \right)}} + \frac{366996649667573283524608 \cos{\left(x \right)}}{5659752752088783975 \sin^{51}{\left(x \right)}} - \frac{160329014038666934208532 \cos{\left(x \right)}}{1886584250696261325 \sin^{53}{\left(x \right)}} + \frac{91722895980188070616984 \cos{\left(x \right)}}{961090089977340675 \sin^{55}{\left(x \right)}} - \frac{1607517633411683617036 \cos{\left(x \right)}}{17474365272315285 \sin^{57}{\left(x \right)}} + \frac{23331419354498899508 \cos{\left(x \right)}}{306567811795005 \sin^{59}{\left(x \right)}} - \frac{4203551791790935423 \cos{\left(x \right)}}{77940969100425 \sin^{61}{\left(x \right)}} + \frac{41667137547699346 \cos{\left(x \right)}}{1277720804925 \sin^{63}{\left(x \right)}} - \frac{2373737631116927 \cos{\left(x \right)}}{141968978325 \sin^{65}{\left(x \right)}} + \frac{6750163959008912 \cos{\left(x \right)}}{936995256945 \sin^{67}{\left(x \right)}} - \frac{36017228877266 \cos{\left(x \right)}}{13985003835 \sin^{69}{\left(x \right)}} + \frac{760433375156 \cos{\left(x \right)}}{1013406075 \sin^{71}{\left(x \right)}} - \frac{22308242918 \cos{\left(x \right)}}{128459925 \sin^{73}{\left(x \right)}} + \frac{54049268 \cos{\left(x \right)}}{1759725 \sin^{75}{\left(x \right)}} - \frac{91507 \cos{\left(x \right)}}{23463 \sin^{77}{\left(x \right)}} + \frac{2026 \cos{\left(x \right)}}{6399 \sin^{79}{\left(x \right)}} - \frac{\cos{\left(x \right)}}{81 \sin^{81}{\left(x \right)}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.