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Resolución de integrales/ cos(nx)/ 2x^4cos(nx)

Integral de 2x^4cos(nx) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 180                
  /                 
 |                  
 |     4            
 |  2*x *cos(n*x) dx
 |                  
/                   
0
∫01802x4cos⁡(nx) dx\int\limits_{0}^{180} 2 x^{4} \cos{\left(n x \right)}\, dx 
Integral((2*x^4)*cos(n*x), (x, 0, 180))
Respuesta (Indefinida) [src] 
                            //                                   5                                             \                              
                            ||                                  x                                              |                              
                            ||                                  --                                    for n = 0|                              
                            ||                                  5                                              |                              
  /                         ||                                                                                 |                              
 |                          ||/                3               2                                               |        //   x      for n = 0\
 |    4                     |||  6*sin(n*x)   x *cos(n*x)   3*x *sin(n*x)   6*x*cos(n*x)                       |      4 ||                   |
 | 2*x *cos(n*x) dx = C - 8*|<|- ---------- - ----------- + ------------- + ------------  for n != 0           | + 2*x *|
∫2x4cos⁡(nx) dx=C+2x4({xfor n=0sin⁡(nx)notherwise)−8({x55for n=0{−x3cos⁡(nx)n+3x2sin⁡(nx)n2+6xcos⁡(nx)n3−6sin⁡(nx)n4for n≠00otherwisenotherwise)\int 2 x^{4} \cos{\left(n x \right)}\, dx = C + 2 x^{4} \left(\begin{cases} x & \text{for}\: n = 0 \\\frac{\sin{\left(n x \right)}}{n} & \text{otherwise} \end{cases}\right) - 8 \left(\begin{cases} \frac{x^{5}}{5} & \text{for}\: n = 0 \\\frac{\begin{cases} - \frac{x^{3} \cos{\left(n x \right)}}{n} + \frac{3 x^{2} \sin{\left(n x \right)}}{n^{2}} + \frac{6 x \cos{\left(n x \right)}}{n^{3}} - \frac{6 \sin{\left(n x \right)}}{n^{4}} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}}{n} & \text{otherwise} \end{cases}\right)
Simplificar
Respuesta [src] 
/  777600*sin(180*n)   8640*cos(180*n)   48*sin(180*n)   46656000*cos(180*n)   2099520000*sin(180*n)                                  
|- ----------------- - --------------- + ------------- + ------------------- + ---------------------  for And(n > -oo, n < oo, n != 0)
|           3                  4                5                  2                     n                                            
<          n                  n                n                  n                                                                   
|                                                                                                                                     
|                                            75582720000                                                         otherwise            
\
{2099520000sin⁡(180n)n+46656000cos⁡(180n)n2−777600sin⁡(180n)n3−8640cos⁡(180n)n4+48sin⁡(180n)n5for n>−∞∧n<∞∧n≠075582720000otherwise\begin{cases} \frac{2099520000 \sin{\left(180 n \right)}}{n} + \frac{46656000 \cos{\left(180 n \right)}}{n^{2}} - \frac{777600 \sin{\left(180 n \right)}}{n^{3}} - \frac{8640 \cos{\left(180 n \right)}}{n^{4}} + \frac{48 \sin{\left(180 n \right)}}{n^{5}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\75582720000 & \text{otherwise} \end{cases} 
=
= 
/  777600*sin(180*n)   8640*cos(180*n)   48*sin(180*n)   46656000*cos(180*n)   2099520000*sin(180*n)                                  
|- ----------------- - --------------- + ------------- + ------------------- + ---------------------  for And(n > -oo, n < oo, n != 0)
|           3                  4                5                  2                     n                                            
<          n                  n                n                  n                                                                   
|                                                                                                                                     
|                                            75582720000                                                         otherwise            
\
{2099520000sin⁡(180n)n+46656000cos⁡(180n)n2−777600sin⁡(180n)n3−8640cos⁡(180n)n4+48sin⁡(180n)n5for n>−∞∧n<∞∧n≠075582720000otherwise\begin{cases} \frac{2099520000 \sin{\left(180 n \right)}}{n} + \frac{46656000 \cos{\left(180 n \right)}}{n^{2}} - \frac{777600 \sin{\left(180 n \right)}}{n^{3}} - \frac{8640 \cos{\left(180 n \right)}}{n^{4}} + \frac{48 \sin{\left(180 n \right)}}{n^{5}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\75582720000 & \text{otherwise} \end{cases} 
Piecewise((-777600*sin(180*n)/n^3 - 8640*cos(180*n)/n^4 + 48*sin(180*n)/n^5 + 46656000*cos(180*n)/n^2 + 2099520000*sin(180*n)/n, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (75582720000, True))

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

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