Sr Examen
Integral de cos^42xdx dx
Solución
Ha introducido
[src]
1 / | | 42 | cos (x) dx | / 0
$$\int\limits_{0}^{1} \cos^{42}{\left(x \right)}\, dx$$
Integral(cos(x)^42, (x, 0, 1))
Gráfica
Respuesta
[src]
41 39 37 33 35 31 29 15 17 25 23 19 13 21 27 11 5 9 7 3 67282234305 cos (1)*sin(1) 41*cos (1)*sin(1) 533*cos (1)*sin(1) 19721*cos (1)*sin(1) 19721*cos (1)*sin(1) 216931*cos (1)*sin(1) 6724861*cos (1)*sin(1) 31367009*cos (1)*sin(1) 31367009*cos (1)*sin(1) 45004839*cos (1)*sin(1) 75008065*cos (1)*sin(1) 94101027*cos (1)*sin(1) 156835045*cos (1)*sin(1) 156835045*cos (1)*sin(1) 195020969*cos (1)*sin(1) 2038855585*cos (1)*sin(1) 4485482287*cos (1)*sin(1) 4485482287*cos (1)*sin(1) 13456446861*cos (1)*sin(1) 22427411435*cos (1)*sin(1) 67282234305*cos(1)*sin(1) ------------ + --------------- + ------------------ + ------------------- + --------------------- + --------------------- + ---------------------- + ----------------------- + ------------------------ + ------------------------ + ------------------------ + ------------------------ + ------------------------ + ------------------------- + ------------------------- + ------------------------- + -------------------------- + ------------------------- + ------------------------- + -------------------------- + -------------------------- + ------------------------- 549755813888 42 1680 21280 744192 766080 7938048 238141440 805306368 855638016 1481768960 2370830336 2709520384 3758096384 4741660672 6667960320 45097156608 68719476736 90194313216 240518168576 274877906944 549755813888
$$\frac{\sin{\left(1 \right)} \cos^{41}{\left(1 \right)}}{42} + \frac{41 \sin{\left(1 \right)} \cos^{39}{\left(1 \right)}}{1680} + \frac{533 \sin{\left(1 \right)} \cos^{37}{\left(1 \right)}}{21280} + \frac{19721 \sin{\left(1 \right)} \cos^{35}{\left(1 \right)}}{766080} + \frac{19721 \sin{\left(1 \right)} \cos^{33}{\left(1 \right)}}{744192} + \frac{216931 \sin{\left(1 \right)} \cos^{31}{\left(1 \right)}}{7938048} + \frac{6724861 \sin{\left(1 \right)} \cos^{29}{\left(1 \right)}}{238141440} + \frac{195020969 \sin{\left(1 \right)} \cos^{27}{\left(1 \right)}}{6667960320} + \frac{45004839 \sin{\left(1 \right)} \cos^{25}{\left(1 \right)}}{1481768960} + \frac{75008065 \sin{\left(1 \right)} \cos^{23}{\left(1 \right)}}{2370830336} + \frac{156835045 \sin{\left(1 \right)} \cos^{21}{\left(1 \right)}}{4741660672} + \frac{94101027 \sin{\left(1 \right)} \cos^{19}{\left(1 \right)}}{2709520384} + \frac{31367009 \sin{\left(1 \right)} \cos^{17}{\left(1 \right)}}{855638016} + \frac{31367009 \sin{\left(1 \right)} \cos^{15}{\left(1 \right)}}{805306368} + \frac{156835045 \sin{\left(1 \right)} \cos^{13}{\left(1 \right)}}{3758096384} + \frac{2038855585 \sin{\left(1 \right)} \cos^{11}{\left(1 \right)}}{45097156608} + \frac{4485482287 \sin{\left(1 \right)} \cos^{9}{\left(1 \right)}}{90194313216} + \frac{13456446861 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{240518168576} + \frac{4485482287 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{68719476736} + \frac{22427411435 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{274877906944} + \frac{67282234305 \sin{\left(1 \right)} \cos{\left(1 \right)}}{549755813888} + \frac{67282234305}{549755813888}$$
=
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41 39 37 33 35 31 29 15 17 25 23 19 13 21 27 11 5 9 7 3 67282234305 cos (1)*sin(1) 41*cos (1)*sin(1) 533*cos (1)*sin(1) 19721*cos (1)*sin(1) 19721*cos (1)*sin(1) 216931*cos (1)*sin(1) 6724861*cos (1)*sin(1) 31367009*cos (1)*sin(1) 31367009*cos (1)*sin(1) 45004839*cos (1)*sin(1) 75008065*cos (1)*sin(1) 94101027*cos (1)*sin(1) 156835045*cos (1)*sin(1) 156835045*cos (1)*sin(1) 195020969*cos (1)*sin(1) 2038855585*cos (1)*sin(1) 4485482287*cos (1)*sin(1) 4485482287*cos (1)*sin(1) 13456446861*cos (1)*sin(1) 22427411435*cos (1)*sin(1) 67282234305*cos(1)*sin(1) ------------ + --------------- + ------------------ + ------------------- + --------------------- + --------------------- + ---------------------- + ----------------------- + ------------------------ + ------------------------ + ------------------------ + ------------------------ + ------------------------ + ------------------------- + ------------------------- + ------------------------- + -------------------------- + ------------------------- + ------------------------- + -------------------------- + -------------------------- + ------------------------- 549755813888 42 1680 21280 744192 766080 7938048 238141440 805306368 855638016 1481768960 2370830336 2709520384 3758096384 4741660672 6667960320 45097156608 68719476736 90194313216 240518168576 274877906944 549755813888
$$\frac{\sin{\left(1 \right)} \cos^{41}{\left(1 \right)}}{42} + \frac{41 \sin{\left(1 \right)} \cos^{39}{\left(1 \right)}}{1680} + \frac{533 \sin{\left(1 \right)} \cos^{37}{\left(1 \right)}}{21280} + \frac{19721 \sin{\left(1 \right)} \cos^{35}{\left(1 \right)}}{766080} + \frac{19721 \sin{\left(1 \right)} \cos^{33}{\left(1 \right)}}{744192} + \frac{216931 \sin{\left(1 \right)} \cos^{31}{\left(1 \right)}}{7938048} + \frac{6724861 \sin{\left(1 \right)} \cos^{29}{\left(1 \right)}}{238141440} + \frac{195020969 \sin{\left(1 \right)} \cos^{27}{\left(1 \right)}}{6667960320} + \frac{45004839 \sin{\left(1 \right)} \cos^{25}{\left(1 \right)}}{1481768960} + \frac{75008065 \sin{\left(1 \right)} \cos^{23}{\left(1 \right)}}{2370830336} + \frac{156835045 \sin{\left(1 \right)} \cos^{21}{\left(1 \right)}}{4741660672} + \frac{94101027 \sin{\left(1 \right)} \cos^{19}{\left(1 \right)}}{2709520384} + \frac{31367009 \sin{\left(1 \right)} \cos^{17}{\left(1 \right)}}{855638016} + \frac{31367009 \sin{\left(1 \right)} \cos^{15}{\left(1 \right)}}{805306368} + \frac{156835045 \sin{\left(1 \right)} \cos^{13}{\left(1 \right)}}{3758096384} + \frac{2038855585 \sin{\left(1 \right)} \cos^{11}{\left(1 \right)}}{45097156608} + \frac{4485482287 \sin{\left(1 \right)} \cos^{9}{\left(1 \right)}}{90194313216} + \frac{13456446861 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{240518168576} + \frac{4485482287 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{68719476736} + \frac{22427411435 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{274877906944} + \frac{67282234305 \sin{\left(1 \right)} \cos{\left(1 \right)}}{549755813888} + \frac{67282234305}{549755813888}$$
67282234305/549755813888 + cos(1)^41*sin(1)/42 + 41*cos(1)^39*sin(1)/1680 + 533*cos(1)^37*sin(1)/21280 + 19721*cos(1)^33*sin(1)/744192 + 19721*cos(1)^35*sin(1)/766080 + 216931*cos(1)^31*sin(1)/7938048 + 6724861*cos(1)^29*sin(1)/238141440 + 31367009*cos(1)^15*sin(1)/805306368 + 31367009*cos(1)^17*sin(1)/855638016 + 45004839*cos(1)^25*sin(1)/1481768960 + 75008065*cos(1)^23*sin(1)/2370830336 + 94101027*cos(1)^19*sin(1)/2709520384 + 156835045*cos(1)^13*sin(1)/3758096384 + 156835045*cos(1)^21*sin(1)/4741660672 + 195020969*cos(1)^27*sin(1)/6667960320 + 2038855585*cos(1)^11*sin(1)/45097156608 + 4485482287*cos(1)^5*sin(1)/68719476736 + 4485482287*cos(1)^9*sin(1)/90194313216 + 13456446861*cos(1)^7*sin(1)/240518168576 + 22427411435*cos(1)^3*sin(1)/274877906944 + 67282234305*cos(1)*sin(1)/549755813888
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.