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Resolución de integrales/ i*n*x/ (x+1)/ (x+1)*(sin((pi*n*x)/2))

Integral de (x+1)*(sin((pi*n*x)/2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  0                       
  /                       
 |                        
 |             /pi*n*x\   
 |  (x + 1)*sin|------| dx
 |             \  2   /   
 |                        
/                         
-2
$$\int\limits_{-2}^{0} \left(x + 1\right) \sin{\left(\frac{x \pi n}{2} \right)}\, dx$$ 
Integral((x + 1)*sin(((pi*n)*x)/2), (x, -2, 0))
Respuesta (Indefinida) [src] 
                                //                0                   for n = 0\                                                                
                                ||                                             |                                                                
  /                             ||   //     /pi*n*x\               \           |     //      0         for n = 0\   //      0         for n = 0\
 |                              ||   ||2*sin|------|               |           |     ||                         |   ||                         |
 |            /pi*n*x\          ||   ||     \  2   /      pi*n     |           |     ||      /pi*n*x\           |   ||      /pi*n*x\           |
 | (x + 1)*sin|------| dx = C - |<-2*|<-------------  for ---- != 0|           | + x*|<-2*cos|------|           | + |<-2*cos|------|           |
 |            \  2   /          ||   ||     pi*n           2       |           |     ||      \  2   /           |   ||      \  2   /           |
 |                              ||   ||                            |           |     ||--------------  otherwise|   ||--------------  otherwise|
/                               ||   \\      x          otherwise  /           |     \\     pi*n                /   \\     pi*n                /
                                ||----------------------------------  otherwise|                                                                
                                \\               pi*n                          /
$$\int \left(x + 1\right) \sin{\left(\frac{x \pi n}{2} \right)}\, dx = C + x \left(\begin{cases} 0 & \text{for}\: n = 0 \\- \frac{2 \cos{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{otherwise} \end{cases}\right) - \begin{cases} 0 & \text{for}\: n = 0 \\- \frac{2 \left(\begin{cases} \frac{2 \sin{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{for}\: \frac{\pi n}{2} \neq 0 \\x & \text{otherwise} \end{cases}\right)}{\pi n} & \text{otherwise} \end{cases} + \begin{cases} 0 & \text{for}\: n = 0 \\- \frac{2 \cos{\left(\frac{\pi n x}{2} \right)}}{\pi n} & \text{otherwise} \end{cases}$$
Simplificar
Respuesta [src] 
/   2     2*cos(pi*n)   4*sin(pi*n)                                  
|- ---- - ----------- + -----------  for And(n > -oo, n < oo, n != 0)
|  pi*n       pi*n           2  2                                    
<                          pi *n                                     
|                                                                    
|                0                              otherwise            
\
$$\begin{cases} - \frac{2 \cos{\left(\pi n \right)}}{\pi n} - \frac{2}{\pi n} + \frac{4 \sin{\left(\pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$ 
=
= 
/   2     2*cos(pi*n)   4*sin(pi*n)                                  
|- ---- - ----------- + -----------  for And(n > -oo, n < oo, n != 0)
|  pi*n       pi*n           2  2                                    
<                          pi *n                                     
|                                                                    
|                0                              otherwise            
\
$$\begin{cases} - \frac{2 \cos{\left(\pi n \right)}}{\pi n} - \frac{2}{\pi n} + \frac{4 \sin{\left(\pi n \right)}}{\pi^{2} n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$ 
Piecewise((-2/(pi*n) - 2*cos(pi*n)/(pi*n) + 4*sin(pi*n)/(pi^2*n^2), (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))

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

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