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Resolución de integrales/ cos^4/ cos^42xdx

Integral de cos^42xdx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |     42      
 |  cos  (x) dx
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/              
0
∫01cos⁡42(x) dx\int\limits_{0}^{1} \cos^{42}{\left(x \right)}\, dx 
Integral(cos(x)^42, (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
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
sin⁡(1)cos⁡41(1)42+41sin⁡(1)cos⁡39(1)1680+533sin⁡(1)cos⁡37(1)21280+19721sin⁡(1)cos⁡35(1)766080+19721sin⁡(1)cos⁡33(1)744192+216931sin⁡(1)cos⁡31(1)7938048+6724861sin⁡(1)cos⁡29(1)238141440+195020969sin⁡(1)cos⁡27(1)6667960320+45004839sin⁡(1)cos⁡25(1)1481768960+75008065sin⁡(1)cos⁡23(1)2370830336+156835045sin⁡(1)cos⁡21(1)4741660672+94101027sin⁡(1)cos⁡19(1)2709520384+31367009sin⁡(1)cos⁡17(1)855638016+31367009sin⁡(1)cos⁡15(1)805306368+156835045sin⁡(1)cos⁡13(1)3758096384+2038855585sin⁡(1)cos⁡11(1)45097156608+4485482287sin⁡(1)cos⁡9(1)90194313216+13456446861sin⁡(1)cos⁡7(1)240518168576+4485482287sin⁡(1)cos⁡5(1)68719476736+22427411435sin⁡(1)cos⁡3(1)274877906944+67282234305sin⁡(1)cos⁡(1)549755813888+67282234305549755813888\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} 
=
= 
                  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
sin⁡(1)cos⁡41(1)42+41sin⁡(1)cos⁡39(1)1680+533sin⁡(1)cos⁡37(1)21280+19721sin⁡(1)cos⁡35(1)766080+19721sin⁡(1)cos⁡33(1)744192+216931sin⁡(1)cos⁡31(1)7938048+6724861sin⁡(1)cos⁡29(1)238141440+195020969sin⁡(1)cos⁡27(1)6667960320+45004839sin⁡(1)cos⁡25(1)1481768960+75008065sin⁡(1)cos⁡23(1)2370830336+156835045sin⁡(1)cos⁡21(1)4741660672+94101027sin⁡(1)cos⁡19(1)2709520384+31367009sin⁡(1)cos⁡17(1)855638016+31367009sin⁡(1)cos⁡15(1)805306368+156835045sin⁡(1)cos⁡13(1)3758096384+2038855585sin⁡(1)cos⁡11(1)45097156608+4485482287sin⁡(1)cos⁡9(1)90194313216+13456446861sin⁡(1)cos⁡7(1)240518168576+4485482287sin⁡(1)cos⁡5(1)68719476736+22427411435sin⁡(1)cos⁡3(1)274877906944+67282234305sin⁡(1)cos⁡(1)549755813888+67282234305549755813888\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
Respuesta numérica [src] 
0.192242962848103
0.192242962848103

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