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Resolución de integrales/ sin(x)/ cos^5/ (sin(x)*x*dx)/(cos^5*x)

Integral de (sin(x)*x*dx)/(cos^5*x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |  sin(x)*x   
 |  -------- dx
 |     5       
 |  cos (x)    
 |             
/              
0
∫01xsin⁡(x)cos⁡5(x) dx\int\limits_{0}^{1} \frac{x \sin{\left(x \right)}}{\cos^{5}{\left(x \right)}}\, dx 
Integral((sin(x)*x)/cos(x)^5, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                              5/x\                                                     /x\                                                                                                              7/x\                                                      3/x\                                                     8/x\                                                      2/x\                                                     6/x\                                                     4/x\                     
 |                                         10*tan |-|                                                6*tan|-|                                                                                                         6*tan |-|                                                10*tan |-|                                              3*x*tan |-|                                              12*x*tan |-|                                             12*x*tan |-|                                             18*x*tan |-|                     
 | sin(x)*x                                       \2/                                                     \2/                                                   3*x                                                         \2/                                                       \2/                                                      \2/                                                       \2/                                                      \2/                                                      \2/                     
 | -------- dx = C - ------------------------------------------------------ - ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------
 |    5                         2/x\         6/x\         8/x\         4/x\              2/x\         6/x\         8/x\         4/x\              2/x\         6/x\         8/x\         4/x\              2/x\         6/x\         8/x\         4/x\              2/x\         6/x\         8/x\         4/x\              2/x\         6/x\         8/x\         4/x\              2/x\         6/x\         8/x\         4/x\              2/x\         6/x\         8/x\         4/x\              2/x\         6/x\         8/x\         4/x\
 | cos (x)           12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-|   12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-|   12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-|   12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-|   12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-|   12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-|   12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-|   12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-|   12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-|
 |                               \2/          \2/          \2/          \2/               \2/          \2/          \2/          \2/               \2/          \2/          \2/          \2/               \2/          \2/          \2/          \2/               \2/          \2/          \2/          \2/               \2/          \2/          \2/          \2/               \2/          \2/          \2/          \2/               \2/          \2/          \2/          \2/               \2/          \2/          \2/          \2/
/
∫xsin⁡(x)cos⁡5(x) dx=C+3xtan⁡8(x2)12tan⁡8(x2)−48tan⁡6(x2)+72tan⁡4(x2)−48tan⁡2(x2)+12+12xtan⁡6(x2)12tan⁡8(x2)−48tan⁡6(x2)+72tan⁡4(x2)−48tan⁡2(x2)+12+18xtan⁡4(x2)12tan⁡8(x2)−48tan⁡6(x2)+72tan⁡4(x2)−48tan⁡2(x2)+12+12xtan⁡2(x2)12tan⁡8(x2)−48tan⁡6(x2)+72tan⁡4(x2)−48tan⁡2(x2)+12+3x12tan⁡8(x2)−48tan⁡6(x2)+72tan⁡4(x2)−48tan⁡2(x2)+12+6tan⁡7(x2)12tan⁡8(x2)−48tan⁡6(x2)+72tan⁡4(x2)−48tan⁡2(x2)+12−10tan⁡5(x2)12tan⁡8(x2)−48tan⁡6(x2)+72tan⁡4(x2)−48tan⁡2(x2)+12+10tan⁡3(x2)12tan⁡8(x2)−48tan⁡6(x2)+72tan⁡4(x2)−48tan⁡2(x2)+12−6tan⁡(x2)12tan⁡8(x2)−48tan⁡6(x2)+72tan⁡4(x2)−48tan⁡2(x2)+12\int \frac{x \sin{\left(x \right)}}{\cos^{5}{\left(x \right)}}\, dx = C + \frac{3 x \tan^{8}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{12 x \tan^{6}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{18 x \tan^{4}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{12 x \tan^{2}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{3 x}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{6 \tan^{7}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} - \frac{10 \tan^{5}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{10 \tan^{3}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} - \frac{6 \tan{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90020
Trazar el gráfico f(x)
Respuesta [src] 
                                                                                                5                                                                                                                                8                                                                7                                                                 3                                                                2                                                                6                                                                4                              
                              3                                                           10*tan (1/2)                                                      6*tan(1/2)                                                      3*tan (1/2)                                                      6*tan (1/2)                                                      10*tan (1/2)                                                     12*tan (1/2)                                                     12*tan (1/2)                                                     18*tan (1/2)                         
-------------------------------------------------------------- - -------------------------------------------------------------- - -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + --------------------------------------------------------------
           2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4     
12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)
−6tan⁡(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12−10tan⁡5(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+3tan⁡8(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+6tan⁡7(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+12tan⁡6(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+18tan⁡4(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+10tan⁡3(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+3−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+12tan⁡2(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12- \frac{6 \tan{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} - \frac{10 \tan^{5}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{3 \tan^{8}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{6 \tan^{7}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{12 \tan^{6}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{18 \tan^{4}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{10 \tan^{3}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{3}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{12 \tan^{2}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} 
=
= 
                                                                                                5                                                                                                                                8                                                                7                                                                 3                                                                2                                                                6                                                                4                              
                              3                                                           10*tan (1/2)                                                      6*tan(1/2)                                                      3*tan (1/2)                                                      6*tan (1/2)                                                      10*tan (1/2)                                                     12*tan (1/2)                                                     12*tan (1/2)                                                     18*tan (1/2)                         
-------------------------------------------------------------- - -------------------------------------------------------------- - -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + --------------------------------------------------------------
           2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4                   2              6              8              4     
12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)   12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)
−6tan⁡(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12−10tan⁡5(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+3tan⁡8(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+6tan⁡7(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+12tan⁡6(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+18tan⁡4(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+10tan⁡3(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+3−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12+12tan⁡2(12)−48tan⁡2(12)−48tan⁡6(12)+12tan⁡8(12)+72tan⁡4(12)+12- \frac{6 \tan{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} - \frac{10 \tan^{5}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{3 \tan^{8}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{6 \tan^{7}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{12 \tan^{6}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{18 \tan^{4}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{10 \tan^{3}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{3}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{12 \tan^{2}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} 
3/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) - 10*tan(1/2)^5/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) - 6*tan(1/2)/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 3*tan(1/2)^8/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 6*tan(1/2)^7/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 10*tan(1/2)^3/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 12*tan(1/2)^2/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 12*tan(1/2)^6/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 18*tan(1/2)^4/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4)
Respuesta numérica [src] 
2.22939938778925
2.22939938778925

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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