Integral de (sin(x)*x*dx)/(cos^5*x) dx
Solución
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/
/
∫cos5(x)xsin(x)dx=C+12tan8(2x)−48tan6(2x)+72tan4(2x)−48tan2(2x)+123xtan8(2x)+12tan8(2x)−48tan6(2x)+72tan4(2x)−48tan2(2x)+1212xtan6(2x)+12tan8(2x)−48tan6(2x)+72tan4(2x)−48tan2(2x)+1218xtan4(2x)+12tan8(2x)−48tan6(2x)+72tan4(2x)−48tan2(2x)+1212xtan2(2x)+12tan8(2x)−48tan6(2x)+72tan4(2x)−48tan2(2x)+123x+12tan8(2x)−48tan6(2x)+72tan4(2x)−48tan2(2x)+126tan7(2x)−12tan8(2x)−48tan6(2x)+72tan4(2x)−48tan2(2x)+1210tan5(2x)+12tan8(2x)−48tan6(2x)+72tan4(2x)−48tan2(2x)+1210tan3(2x)−12tan8(2x)−48tan6(2x)+72tan4(2x)−48tan2(2x)+126tan(2x)
Gráfica
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)
−−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+126tan(21)−−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1210tan5(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+123tan8(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+126tan7(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1212tan6(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1218tan4(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1210tan3(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+123+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1212tan2(21)
=
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)
−−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+126tan(21)−−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1210tan5(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+123tan8(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+126tan7(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1212tan6(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1218tan4(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1210tan3(21)+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+123+−48tan2(21)−48tan6(21)+12tan8(21)+72tan4(21)+1212tan2(21)
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)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.