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Resolución de integrales/ e^(t*(-s))/ cosh(3*t)*e^(t*(-s))

Integral de cosh(3*t)*e^(t*(-s)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |             t*(-s)   
 |  cosh(3*t)*E       dt
 |                      
/                       
0
$$\int\limits_{0}^{1} e^{- s t} \cosh{\left(3 t \right)}\, dt$$ 
Integral(cosh(3*t)*E^(t*(-s)), (t, 0, 1))
Respuesta (Indefinida) [src] 
                              //             3*t                3*t      3*t                         \
                              ||  cosh(3*t)*e      t*cosh(3*t)*e      t*e   *sinh(3*t)               |
                              ||  -------------- + ---------------- - ----------------     for s = -3|
                              ||        6                 2                  2                       |
  /                           ||                                                                     |
 |                            ||             -3*t                -3*t      -3*t                      |
 |            t*(-s)          ||  cosh(3*t)*e       t*cosh(3*t)*e       t*e    *sinh(3*t)            |
 | cosh(3*t)*E       dt = C + |<- --------------- + ----------------- + -----------------  for s = 3 |
 |                            ||         6                  2                   2                    |
/                             ||                                                                     |
                              ||             3*sinh(3*t)          s*cosh(3*t)                        |
                              ||        - ------------------ - ------------------          otherwise |
                              ||               s*t    2  s*t        s*t    2  s*t                    |
                              ||          - 9*e    + s *e      - 9*e    + s *e                       |
                              \\                                                                     /
$$\int e^{- s t} \cosh{\left(3 t \right)}\, dt = C + \begin{cases} - \frac{t e^{3 t} \sinh{\left(3 t \right)}}{2} + \frac{t e^{3 t} \cosh{\left(3 t \right)}}{2} + \frac{e^{3 t} \cosh{\left(3 t \right)}}{6} & \text{for}\: s = -3 \\\frac{t e^{- 3 t} \sinh{\left(3 t \right)}}{2} + \frac{t e^{- 3 t} \cosh{\left(3 t \right)}}{2} - \frac{e^{- 3 t} \cosh{\left(3 t \right)}}{6} & \text{for}\: s = 3 \\- \frac{s \cosh{\left(3 t \right)}}{s^{2} e^{s t} - 9 e^{s t}} - \frac{3 \sinh{\left(3 t \right)}}{s^{2} e^{s t} - 9 e^{s t}} & \text{otherwise} \end{cases}$$
Simplificar
Respuesta [src] 
/                  3    3                             
|         cosh(3)*e    e *sinh(3)                     
|         ---------- - ----------           for s = -3
|             2            3                          
|                                                     
|                -3      -3                           
|       cosh(3)*e     2*e  *sinh(3)                   
<       ----------- + -------------         for s = 3 
|            2              3                         
|                                                     
|   s        3*sinh(3)        s*cosh(3)               
|------- - -------------- - --------------  otherwise 
|      2        s    2  s        s    2  s            
|-9 + s    - 9*e  + s *e    - 9*e  + s *e             
\
$$\begin{cases} - \frac{e^{3} \sinh{\left(3 \right)}}{3} + \frac{e^{3} \cosh{\left(3 \right)}}{2} & \text{for}\: s = -3 \\\frac{\cosh{\left(3 \right)}}{2 e^{3}} + \frac{2 \sinh{\left(3 \right)}}{3 e^{3}} & \text{for}\: s = 3 \\- \frac{s \cosh{\left(3 \right)}}{s^{2} e^{s} - 9 e^{s}} + \frac{s}{s^{2} - 9} - \frac{3 \sinh{\left(3 \right)}}{s^{2} e^{s} - 9 e^{s}} & \text{otherwise} \end{cases}$$ 
=
= 
/                  3    3                             
|         cosh(3)*e    e *sinh(3)                     
|         ---------- - ----------           for s = -3
|             2            3                          
|                                                     
|                -3      -3                           
|       cosh(3)*e     2*e  *sinh(3)                   
<       ----------- + -------------         for s = 3 
|            2              3                         
|                                                     
|   s        3*sinh(3)        s*cosh(3)               
|------- - -------------- - --------------  otherwise 
|      2        s    2  s        s    2  s            
|-9 + s    - 9*e  + s *e    - 9*e  + s *e             
\
$$\begin{cases} - \frac{e^{3} \sinh{\left(3 \right)}}{3} + \frac{e^{3} \cosh{\left(3 \right)}}{2} & \text{for}\: s = -3 \\\frac{\cosh{\left(3 \right)}}{2 e^{3}} + \frac{2 \sinh{\left(3 \right)}}{3 e^{3}} & \text{for}\: s = 3 \\- \frac{s \cosh{\left(3 \right)}}{s^{2} e^{s} - 9 e^{s}} + \frac{s}{s^{2} - 9} - \frac{3 \sinh{\left(3 \right)}}{s^{2} e^{s} - 9 e^{s}} & \text{otherwise} \end{cases}$$ 
Piecewise((cosh(3)*exp(3)/2 - exp(3)*sinh(3)/3, s = -3), (cosh(3)*exp(-3)/2 + 2*exp(-3)*sinh(3)/3, s = 3), (s/(-9 + s^2) - 3*sinh(3)/(-9*exp(s) + s^2*exp(s)) - s*cosh(3)/(-9*exp(s) + s^2*exp(s)), True))

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

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