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Simplificación de expresiones/ Descomposición en fracciones simples/ (16-16*cos(pi*n/4)-16*cos(3*pi*n/4)+16*cos(pi*n)-4*pi*n*sin(pi*n/2)-4*pi*n*sin(3*pi*n/4)+12*pi*n*sin(pi*n))/(pi^2*n^2)+4*(4-4*cos(pi*n/4)+4*cos(pi*n*t/4)+pi*n*(-sin(pi*n/2)+sin(3*pi*n/4))-pi*n*(1-t)*sin(pi*n*t/4))/(pi^2*n^2)

¿Cómo vas a descomponer esta (16-16*cos(pi*n/4)-16*cos(3*pi*n/4)+16*cos(pi*n)-4*pi*n*sin(pi*n/2)-4*pi*n*sin(3*pi*n/4)+12*pi*n*sin(pi*n))/(pi^2*n^2)+4*(4-4*cos(pi*n/4)+4*cos(pi*n*t/4)+pi*n*(-sin(pi*n/2)+sin(3*pi*n/4))-pi*n*(1-t)*sin(pi*n*t/4))/(pi^2*n^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
           /pi*n\         /3*pi*n\                            /pi*n\             /3*pi*n\                         /         /pi*n\        /pi*n*t\        /     /pi*n\      /3*pi*n\\                   /pi*n*t\\
16 - 16*cos|----| - 16*cos|------| + 16*cos(pi*n) - 4*pi*n*sin|----| - 4*pi*n*sin|------| + 12*pi*n*sin(pi*n)   4*|4 - 4*cos|----| + 4*cos|------| + pi*n*|- sin|----| + sin|------|| - pi*n*(1 - t)*sin|------||
           \ 4  /         \  4   /                            \ 2  /             \  4   /                         \         \ 4  /        \  4   /        \     \ 2  /      \  4   //                   \  4   //
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                                                      2  2                                                                                                      2  2                                             
                                                    pi *n                                                                                                     pi *n
$$\frac{12 \pi n \sin{\left(\pi n \right)} + \left(- 4 \pi n \sin{\left(\frac{3 \pi n}{4} \right)} + \left(- 4 \pi n \sin{\left(\frac{\pi n}{2} \right)} + \left(\left(\left(16 - 16 \cos{\left(\frac{\pi n}{4} \right)}\right) - 16 \cos{\left(\frac{3 \pi n}{4} \right)}\right) + 16 \cos{\left(\pi n \right)}\right)\right)\right)}{\pi^{2} n^{2}} + \frac{4 \left(- \pi n \left(1 - t\right) \sin{\left(\frac{t \pi n}{4} \right)} + \left(\pi n \left(- \sin{\left(\frac{\pi n}{2} \right)} + \sin{\left(\frac{3 \pi n}{4} \right)}\right) + \left(\left(4 - 4 \cos{\left(\frac{\pi n}{4} \right)}\right) + 4 \cos{\left(\frac{t \pi n}{4} \right)}\right)\right)\right)}{\pi^{2} n^{2}}$$ 
(16 - 16*cos((pi*n)/4) - 16*cos(((3*pi)*n)/4) + 16*cos(pi*n) - (4*pi)*n*sin((pi*n)/2) - (4*pi)*n*sin(((3*pi)*n)/4) + ((12*pi)*n)*sin(pi*n))/((pi^2*n^2)) + (4*(4 - 4*cos((pi*n)/4) + 4*cos(((pi*n)*t)/4) + (pi*n)*(-sin((pi*n)/2) + sin(((3*pi)*n)/4)) - (pi*n)*(1 - t)*sin(((pi*n)*t)/4)))/((pi^2*n^2))
Simplificación general [src] 
  /         /pi*n\        /3*pi*n\                      /pi*n*t\           /pi*n*t\             /pi*n\                                /pi*n*t\\
4*|8 - 8*cos|----| - 4*cos|------| + 4*cos(pi*n) + 4*cos|------| - pi*n*sin|------| - 2*pi*n*sin|----| + 3*pi*n*sin(pi*n) + pi*n*t*sin|------||
  \         \ 4  /        \  4   /                      \  4   /           \  4   /             \ 2  /                                \  4   //
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                                                                       2  2                                                                    
                                                                     pi *n
$$\frac{4 \left(\pi n t \sin{\left(\frac{\pi n t}{4} \right)} - 2 \pi n \sin{\left(\frac{\pi n}{2} \right)} + 3 \pi n \sin{\left(\pi n \right)} - \pi n \sin{\left(\frac{\pi n t}{4} \right)} - 8 \cos{\left(\frac{\pi n}{4} \right)} - 4 \cos{\left(\frac{3 \pi n}{4} \right)} + 4 \cos{\left(\pi n \right)} + 4 \cos{\left(\frac{\pi n t}{4} \right)} + 8\right)}{\pi^{2} n^{2}}$$ 
4*(8 - 8*cos(pi*n/4) - 4*cos(3*pi*n/4) + 4*cos(pi*n) + 4*cos(pi*n*t/4) - pi*n*sin(pi*n*t/4) - 2*pi*n*sin(pi*n/2) + 3*pi*n*sin(pi*n) + pi*n*t*sin(pi*n*t/4))/(pi^2*n^2)
Combinatoria [src] 
  /         /pi*n\        /3*pi*n\                      /pi*n*t\           /pi*n*t\             /pi*n\                                /pi*n*t\\
4*|8 - 8*cos|----| - 4*cos|------| + 4*cos(pi*n) + 4*cos|------| - pi*n*sin|------| - 2*pi*n*sin|----| + 3*pi*n*sin(pi*n) + pi*n*t*sin|------||
  \         \ 4  /        \  4   /                      \  4   /           \  4   /             \ 2  /                                \  4   //
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                                                                       2  2                                                                    
                                                                     pi *n
$$\frac{4 \left(\pi n t \sin{\left(\frac{\pi n t}{4} \right)} - 2 \pi n \sin{\left(\frac{\pi n}{2} \right)} + 3 \pi n \sin{\left(\pi n \right)} - \pi n \sin{\left(\frac{\pi n t}{4} \right)} - 8 \cos{\left(\frac{\pi n}{4} \right)} - 4 \cos{\left(\frac{3 \pi n}{4} \right)} + 4 \cos{\left(\pi n \right)} + 4 \cos{\left(\frac{\pi n t}{4} \right)} + 8\right)}{\pi^{2} n^{2}}$$ 
4*(8 - 8*cos(pi*n/4) - 4*cos(3*pi*n/4) + 4*cos(pi*n) + 4*cos(pi*n*t/4) - pi*n*sin(pi*n*t/4) - 2*pi*n*sin(pi*n/2) + 3*pi*n*sin(pi*n) + pi*n*t*sin(pi*n*t/4))/(pi^2*n^2)
Unión de expresiones racionales [src] 
  /         /pi*n\        /3*pi*n\                      /pi*n*t\        /     /pi*n\      /3*pi*n\\           /pi*n\           /3*pi*n\                                      /pi*n*t\\
4*|8 - 8*cos|----| - 4*cos|------| + 4*cos(pi*n) + 4*cos|------| + pi*n*|- sin|----| + sin|------|| - pi*n*sin|----| - pi*n*sin|------| + 3*pi*n*sin(pi*n) - pi*n*(1 - t)*sin|------||
  \         \ 4  /        \  4   /                      \  4   /        \     \ 2  /      \  4   //           \ 2  /           \  4   /                                      \  4   //
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                                                                                          2  2                                                                                        
                                                                                        pi *n
$$\frac{4 \left(- \pi n \left(1 - t\right) \sin{\left(\frac{\pi n t}{4} \right)} + \pi n \left(- \sin{\left(\frac{\pi n}{2} \right)} + \sin{\left(\frac{3 \pi n}{4} \right)}\right) - \pi n \sin{\left(\frac{\pi n}{2} \right)} - \pi n \sin{\left(\frac{3 \pi n}{4} \right)} + 3 \pi n \sin{\left(\pi n \right)} - 8 \cos{\left(\frac{\pi n}{4} \right)} - 4 \cos{\left(\frac{3 \pi n}{4} \right)} + 4 \cos{\left(\pi n \right)} + 4 \cos{\left(\frac{\pi n t}{4} \right)} + 8\right)}{\pi^{2} n^{2}}$$ 
4*(8 - 8*cos(pi*n/4) - 4*cos(3*pi*n/4) + 4*cos(pi*n) + 4*cos(pi*n*t/4) + pi*n*(-sin(pi*n/2) + sin(3*pi*n/4)) - pi*n*sin(pi*n/2) - pi*n*sin(3*pi*n/4) + 3*pi*n*sin(pi*n) - pi*n*(1 - t)*sin(pi*n*t/4))/(pi^2*n^2)
Respuesta numérica [src] 
0.101321183642338*(16.0 + 16.0*cos(((pi*n)*t)/4) - 16.0*cos((pi*n)/4) + 12.5663706143592*n*(-sin((pi*n)/2) + sin(((3*pi)*n)/4)) - 12.5663706143592*n*(1.0 - t)*sin(((pi*n)*t)/4))/n^2 + 0.101321183642338*(16.0 + 16.0*cos(pi*n) - 16.0*cos((pi*n)/4) - 16.0*cos(((3*pi)*n)/4) + 37.6991118430775*n*sin(pi*n) - 12.5663706143592*n*sin((pi*n)/2) - 12.5663706143592*n*sin(((3*pi)*n)/4))/n^2
0.101321183642338*(16.0 + 16.0*cos(((pi*n)*t)/4) - 16.0*cos((pi*n)/4) + 12.5663706143592*n*(-sin((pi*n)/2) + sin(((3*pi)*n)/4)) - 12.5663706143592*n*(1.0 - t)*sin(((pi*n)*t)/4))/n^2 + 0.101321183642338*(16.0 + 16.0*cos(pi*n) - 16.0*cos((pi*n)/4) - 16.0*cos(((3*pi)*n)/4) + 37.6991118430775*n*sin(pi*n) - 12.5663706143592*n*sin((pi*n)/2) - 12.5663706143592*n*sin(((3*pi)*n)/4))/n^2
Denominador racional [src] 
           /pi*n\         /3*pi*n\                        /pi*n*t\             /pi*n\             /pi*n*t\                                   /pi*n*t\
32 - 32*cos|----| - 16*cos|------| + 16*cos(pi*n) + 16*cos|------| - 8*pi*n*sin|----| - 4*pi*n*sin|------| + 12*pi*n*sin(pi*n) + 4*pi*n*t*sin|------|
           \ 4  /         \  4   /                        \  4   /             \ 2  /             \  4   /                                   \  4   /
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                                                                          2  2                                                                       
                                                                        pi *n
$$\frac{4 \pi n t \sin{\left(\frac{\pi n t}{4} \right)} - 8 \pi n \sin{\left(\frac{\pi n}{2} \right)} + 12 \pi n \sin{\left(\pi n \right)} - 4 \pi n \sin{\left(\frac{\pi n t}{4} \right)} - 32 \cos{\left(\frac{\pi n}{4} \right)} - 16 \cos{\left(\frac{3 \pi n}{4} \right)} + 16 \cos{\left(\pi n \right)} + 16 \cos{\left(\frac{\pi n t}{4} \right)} + 32}{\pi^{2} n^{2}}$$ 
(32 - 32*cos(pi*n/4) - 16*cos(3*pi*n/4) + 16*cos(pi*n) + 16*cos(pi*n*t/4) - 8*pi*n*sin(pi*n/2) - 4*pi*n*sin(pi*n*t/4) + 12*pi*n*sin(pi*n) + 4*pi*n*t*sin(pi*n*t/4))/(pi^2*n^2)
Denominador común [src] 
           /pi*n\         /3*pi*n\                        /pi*n*t\             /pi*n\             /pi*n*t\                                   /pi*n*t\
32 - 32*cos|----| - 16*cos|------| + 16*cos(pi*n) + 16*cos|------| - 8*pi*n*sin|----| - 4*pi*n*sin|------| + 12*pi*n*sin(pi*n) + 4*pi*n*t*sin|------|
           \ 4  /         \  4   /                        \  4   /             \ 2  /             \  4   /                                   \  4   /
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                                                                          2  2                                                                       
                                                                        pi *n
$$\frac{4 \pi n t \sin{\left(\frac{\pi n t}{4} \right)} - 8 \pi n \sin{\left(\frac{\pi n}{2} \right)} + 12 \pi n \sin{\left(\pi n \right)} - 4 \pi n \sin{\left(\frac{\pi n t}{4} \right)} - 32 \cos{\left(\frac{\pi n}{4} \right)} - 16 \cos{\left(\frac{3 \pi n}{4} \right)} + 16 \cos{\left(\pi n \right)} + 16 \cos{\left(\frac{\pi n t}{4} \right)} + 32}{\pi^{2} n^{2}}$$ 
(32 - 32*cos(pi*n/4) - 16*cos(3*pi*n/4) + 16*cos(pi*n) + 16*cos(pi*n*t/4) - 8*pi*n*sin(pi*n/2) - 4*pi*n*sin(pi*n*t/4) + 12*pi*n*sin(pi*n) + 4*pi*n*t*sin(pi*n*t/4))/(pi^2*n^2)
Potencias [src] 
           /pi*n\         /pi*n*t\          /     /pi*n\      /3*pi*n\\                     /pi*n*t\              /pi*n\         /3*pi*n\                            /pi*n\             /3*pi*n\                    
16 - 16*cos|----| + 16*cos|------| + 4*pi*n*|- sin|----| + sin|------|| - 4*pi*n*(1 - t)*sin|------|   16 - 16*cos|----| - 16*cos|------| + 16*cos(pi*n) - 4*pi*n*sin|----| - 4*pi*n*sin|------| + 12*pi*n*sin(pi*n)
           \ 4  /         \  4   /          \     \ 2  /      \  4   //                     \  4   /              \ 4  /         \  4   /                            \ 2  /             \  4   /                    
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                                                 2  2                                                                                                        2  2                                                   
                                               pi *n                                                                                                       pi *n
$$\frac{- 4 \pi n \left(1 - t\right) \sin{\left(\frac{\pi n t}{4} \right)} + 4 \pi n \left(- \sin{\left(\frac{\pi n}{2} \right)} + \sin{\left(\frac{3 \pi n}{4} \right)}\right) - 16 \cos{\left(\frac{\pi n}{4} \right)} + 16 \cos{\left(\frac{\pi n t}{4} \right)} + 16}{\pi^{2} n^{2}} + \frac{- 4 \pi n \sin{\left(\frac{\pi n}{2} \right)} - 4 \pi n \sin{\left(\frac{3 \pi n}{4} \right)} + 12 \pi n \sin{\left(\pi n \right)} - 16 \cos{\left(\frac{\pi n}{4} \right)} - 16 \cos{\left(\frac{3 \pi n}{4} \right)} + 16 \cos{\left(\pi n \right)} + 16}{\pi^{2} n^{2}}$$ 
                                                                    /  /   -pi*I*n     pi*I*n\     /   -3*pi*I*n    3*pi*I*n\\                                                                                                                                                                                                                                               
        -pi*I*n       pi*I*n      -pi*I*n*t       pi*I*n*t          |  |   --------    ------|     |   ---------    --------||                    /   -pi*I*n*t     pi*I*n*t\                                                                                                                                                                                                
        --------      ------      ----------      --------          |  |      2          2   |     |       4           4    ||                    |   ----------    --------|           -3*pi*I*n      -pi*I*n       pi*I*n      3*pi*I*n                                                                       /   -3*pi*I*n    3*pi*I*n\            /   -pi*I*n     pi*I*n\
           4            4             4              4              |I*\- e         + e      /   I*\- e          + e        /|                    |       4            4    |           ---------      --------      ------      --------                                                                       |   ---------    --------|            |   --------    ------|
16 - 8*e         - 8*e       + 8*e           + 8*e         + 4*pi*n*|------------------------- - ----------------------------| + 2*pi*I*n*(1 - t)*\- e           + e        /               4             4            4            4          pi*I*n      -pi*I*n            /   -pi*I*n    pi*I*n\            |       4           4    |            |      2          2   |
                                                                    \            2                            2              /                                                  16 - 8*e          - 8*e         - 8*e       - 8*e         + 8*e       + 8*e        - 6*pi*I*n*\- e        + e      / + 2*pi*I*n*\- e          + e        / + 2*pi*I*n*\- e         + e      /
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                                                                                      2  2                                                                                                                                                                                    2  2                                                                                           
                                                                                    pi *n                                                                                                                                                                                   pi *n
$$\frac{2 i \pi n \left(1 - t\right) \left(e^{\frac{i \pi n t}{4}} - e^{- \frac{i \pi n t}{4}}\right) + 4 \pi n \left(\frac{i \left(e^{\frac{i \pi n}{2}} - e^{- \frac{i \pi n}{2}}\right)}{2} - \frac{i \left(e^{\frac{3 i \pi n}{4}} - e^{- \frac{3 i \pi n}{4}}\right)}{2}\right) - 8 e^{\frac{i \pi n}{4}} + 8 e^{\frac{i \pi n t}{4}} + 16 + 8 e^{- \frac{i \pi n t}{4}} - 8 e^{- \frac{i \pi n}{4}}}{\pi^{2} n^{2}} + \frac{2 i \pi n \left(e^{\frac{i \pi n}{2}} - e^{- \frac{i \pi n}{2}}\right) + 2 i \pi n \left(e^{\frac{3 i \pi n}{4}} - e^{- \frac{3 i \pi n}{4}}\right) - 6 i \pi n \left(e^{i \pi n} - e^{- i \pi n}\right) - 8 e^{\frac{3 i \pi n}{4}} - 8 e^{\frac{i \pi n}{4}} + 8 e^{i \pi n} + 16 + 8 e^{- i \pi n} - 8 e^{- \frac{i \pi n}{4}} - 8 e^{- \frac{3 i \pi n}{4}}}{\pi^{2} n^{2}}$$ 
(16 - 8*exp(-pi*i*n/4) - 8*exp(pi*i*n/4) + 8*exp(-pi*i*n*t/4) + 8*exp(pi*i*n*t/4) + 4*pi*n*(i*(-exp(-pi*i*n/2) + exp(pi*i*n/2))/2 - i*(-exp(-3*pi*i*n/4) + exp(3*pi*i*n/4))/2) + 2*pi*i*n*(1 - t)*(-exp(-pi*i*n*t/4) + exp(pi*i*n*t/4)))/(pi^2*n^2) + (16 - 8*exp(-3*pi*i*n/4) - 8*exp(-pi*i*n/4) - 8*exp(pi*i*n/4) - 8*exp(3*pi*i*n/4) + 8*exp(pi*i*n) + 8*exp(-pi*i*n) - 6*pi*i*n*(-exp(-pi*i*n) + exp(pi*i*n)) + 2*pi*i*n*(-exp(-3*pi*i*n/4) + exp(3*pi*i*n/4)) + 2*pi*i*n*(-exp(-pi*i*n/2) + exp(pi*i*n/2)))/(pi^2*n^2)
Compilar la expresión [src] 
           /pi*n\         /pi*n*t\       /   /     /pi*n\      /3*pi*n\\                 /pi*n*t\\              /pi*n\         /3*pi*n\                    /          /pi*n\           /3*pi*n\                  \
16 - 16*cos|----| + 16*cos|------| + 4*n*|pi*|- sin|----| + sin|------|| - pi*(1 - t)*sin|------||   16 - 16*cos|----| - 16*cos|------| + 16*cos(pi*n) + n*|- 4*pi*sin|----| - 4*pi*sin|------| + 12*pi*sin(pi*n)|
           \ 4  /         \  4   /       \   \     \ 2  /      \  4   //                 \  4   //              \ 4  /         \  4   /                    \          \ 2  /           \  4   /                  /
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                                                 2                                                                                                          2                                                     
                                               pi                                                                                                         pi                                                      
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                                                                                                         2                                                                                                        
                                                                                                        n
$$\frac{\frac{4 n \left(- \pi \left(1 - t\right) \sin{\left(\frac{t \pi n}{4} \right)} + \pi \left(- \sin{\left(\frac{\pi n}{2} \right)} + \sin{\left(\frac{3 \pi n}{4} \right)}\right)\right) - 16 \cos{\left(\frac{\pi n}{4} \right)} + 16 \cos{\left(\frac{t \pi n}{4} \right)} + 16}{\pi^{2}} + \frac{n \left(- 4 \pi \sin{\left(\frac{\pi n}{2} \right)} - 4 \pi \sin{\left(\frac{3 \pi n}{4} \right)} + 12 \pi \sin{\left(\pi n \right)}\right) - 16 \cos{\left(\frac{\pi n}{4} \right)} - 16 \cos{\left(\frac{3 \pi n}{4} \right)} + 16 \cos{\left(\pi n \right)} + 16}{\pi^{2}}}{n^{2}}$$ 
           /pi*n\         /pi*n*t\          /     /pi*n\      /3*pi*n\\                     /pi*n*t\              /pi*n\         /3*pi*n\                            /pi*n\             /3*pi*n\                    
16 - 16*cos|----| + 16*cos|------| + 4*pi*n*|- sin|----| + sin|------|| - 4*pi*n*(1 - t)*sin|------|   16 - 16*cos|----| - 16*cos|------| + 16*cos(pi*n) - 4*pi*n*sin|----| - 4*pi*n*sin|------| + 12*pi*n*sin(pi*n)
           \ 4  /         \  4   /          \     \ 2  /      \  4   //                     \  4   /              \ 4  /         \  4   /                            \ 2  /             \  4   /                    
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                                                 2  2                                                                                                        2  2                                                   
                                               pi *n                                                                                                       pi *n
$$\frac{- 4 \pi n \left(1 - t\right) \sin{\left(\frac{t \pi n}{4} \right)} + 4 \pi n \left(- \sin{\left(\frac{\pi n}{2} \right)} + \sin{\left(\frac{3 \pi n}{4} \right)}\right) - 16 \cos{\left(\frac{\pi n}{4} \right)} + 16 \cos{\left(\frac{t \pi n}{4} \right)} + 16}{\pi^{2} n^{2}} + \frac{- 4 \pi n \sin{\left(\frac{\pi n}{2} \right)} - 4 \pi n \sin{\left(\frac{3 \pi n}{4} \right)} + 12 \pi n \sin{\left(\pi n \right)} - 16 \cos{\left(\frac{\pi n}{4} \right)} - 16 \cos{\left(\frac{3 \pi n}{4} \right)} + 16 \cos{\left(\pi n \right)} + 16}{\pi^{2} n^{2}}$$ 
           /pi*n\         /pi*n*t\       /   /     /pi*n\      /3*pi*n\\                 /pi*n*t\\              /pi*n\         /3*pi*n\                    /          /pi*n\           /3*pi*n\                  \
16 - 16*cos|----| + 16*cos|------| + 4*n*|pi*|- sin|----| + sin|------|| - pi*(1 - t)*sin|------||   16 - 16*cos|----| - 16*cos|------| + 16*cos(pi*n) + n*|- 4*pi*sin|----| - 4*pi*sin|------| + 12*pi*sin(pi*n)|
           \ 4  /         \  4   /       \   \     \ 2  /      \  4   //                 \  4   //              \ 4  /         \  4   /                    \          \ 2  /           \  4   /                  /
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                                                2  2                                                                                                       2  2                                                   
                                              pi *n                                                                                                      pi *n
$$\frac{4 n \left(- \pi \left(1 - t\right) \sin{\left(\frac{t \pi n}{4} \right)} + \pi \left(- \sin{\left(\frac{\pi n}{2} \right)} + \sin{\left(\frac{3 \pi n}{4} \right)}\right)\right) - 16 \cos{\left(\frac{\pi n}{4} \right)} + 16 \cos{\left(\frac{t \pi n}{4} \right)} + 16}{\pi^{2} n^{2}} + \frac{n \left(- 4 \pi \sin{\left(\frac{\pi n}{2} \right)} - 4 \pi \sin{\left(\frac{3 \pi n}{4} \right)} + 12 \pi \sin{\left(\pi n \right)}\right) - 16 \cos{\left(\frac{\pi n}{4} \right)} - 16 \cos{\left(\frac{3 \pi n}{4} \right)} + 16 \cos{\left(\pi n \right)} + 16}{\pi^{2} n^{2}}$$ 
(16 - 16*cos((pi*n)/4) + 16*cos(((pi*n)*t)/4) + 4*n*(pi*(-sin((pi*n)/2) + sin(((3*pi)*n)/4)) - pi*(1 - t)*sin(((pi*n)*t)/4)))/(pi^2*n^2) + (16 - 16*cos((pi*n)/4) - 16*cos(((3*pi)*n)/4) + 16*cos(pi*n) + n*(-4*pi*sin((pi*n)/2) - 4*pi*sin(((3*pi)*n)/4) + 12*pi*sin(pi*n)))/(pi^2*n^2)
Abrimos la expresión [src] 
               /pi*n\         /3*pi*n\        /pi*n\        /pi*n*t\                                       /pi*n*t\          /pi*n*t\
         32*cos|----|   16*cos|------|   8*sin|----|   4*sin|------|                                 16*cos|------|   4*t*sin|------|
  32           \ 4  /         \  4   /        \ 2  /        \  4   /   12*sin(pi*n)   16*cos(pi*n)         \  4   /          \  4   /
------ - ------------ - -------------- - ----------- - ------------- + ------------ + ------------ + -------------- + ---------------
  2  2        2  2            2  2           pi*n           pi*n           pi*n            2  2            2  2             pi*n     
pi *n       pi *n           pi *n                                                        pi *n           pi *n
$$\frac{4 t \sin{\left(\frac{\pi n t}{4} \right)}}{\pi n} - \frac{8 \sin{\left(\frac{\pi n}{2} \right)}}{\pi n} + \frac{12 \sin{\left(\pi n \right)}}{\pi n} - \frac{4 \sin{\left(\frac{\pi n t}{4} \right)}}{\pi n} - \frac{32 \cos{\left(\frac{\pi n}{4} \right)}}{\pi^{2} n^{2}} - \frac{16 \cos{\left(\frac{3 \pi n}{4} \right)}}{\pi^{2} n^{2}} + \frac{16 \cos{\left(\pi n \right)}}{\pi^{2} n^{2}} + \frac{16 \cos{\left(\frac{\pi n t}{4} \right)}}{\pi^{2} n^{2}} + \frac{32}{\pi^{2} n^{2}}$$ 
32/(pi^2*n^2) - 32*cos(pi*n/4)/(pi^2*n^2) - 16*cos(3*pi*n/4)/(pi^2*n^2) - 8*sin(pi*n/2)/(pi*n) - 4*sin(pi*n*t/4)/(pi*n) + 12*sin(pi*n)/(pi*n) + 16*cos(pi*n)/(pi^2*n^2) + 16*cos(pi*n*t/4)/(pi^2*n^2) + 4*t*sin(pi*n*t/4)/(pi*n)
    © Sr Examen