Sr Examen

Otras calculadoras

Resolución de integrales/ cos(t)/ cos(t)*e^(t*(-p))

Integral de cos(t)*e^(t*(-p)) dt

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                  
  /                  
 |                   
 |          t*(-p)   
 |  cos(t)*E       dt
 |                   
/                    
0
∫0∞e−ptcos⁡(t) dt\int\limits_{0}^{\infty} e^{- p t} \cos{\left(t \right)}\, dt 
Integral(cos(t)*E^(t*(-p)), (t, 0, oo))
Respuesta (Indefinida) [src] 
                           //           I*t             I*t        I*t                     \
                           || t*cos(t)*e      I*cos(t)*e      I*t*e   *sin(t)              |
                           || ------------- - ------------- - ---------------    for p = -I|
                           ||       2               2                2                     |
  /                        ||                                                              |
 |                         ||          -I*t             -I*t        -I*t                   |
 |         t*(-p)          ||I*cos(t)*e       t*cos(t)*e       I*t*e    *sin(t)            |
 | cos(t)*E       dt = C + |<-------------- + -------------- + ----------------  for p = I |
 |                         ||      2                2                 2                    |
/                          ||                                                              |
                           ||             sin(t)          p*cos(t)                         |
                           ||         -------------- - --------------            otherwise |
                           ||          2  p*t    p*t    2  p*t    p*t                      |
                           ||         p *e    + e      p *e    + e                         |
                           \\                                                              /
∫e−ptcos⁡(t) dt=C+{−iteitsin⁡(t)2+teitcos⁡(t)2−ieitcos⁡(t)2for p=−iite−itsin⁡(t)2+te−itcos⁡(t)2+ie−itcos⁡(t)2for p=i−pcos⁡(t)p2ept+ept+sin⁡(t)p2ept+eptotherwise\int e^{- p t} \cos{\left(t \right)}\, dt = C + \begin{cases} - \frac{i t e^{i t} \sin{\left(t \right)}}{2} + \frac{t e^{i t} \cos{\left(t \right)}}{2} - \frac{i e^{i t} \cos{\left(t \right)}}{2} & \text{for}\: p = - i \\\frac{i t e^{- i t} \sin{\left(t \right)}}{2} + \frac{t e^{- i t} \cos{\left(t \right)}}{2} + \frac{i e^{- i t} \cos{\left(t \right)}}{2} & \text{for}\: p = i \\- \frac{p \cos{\left(t \right)}}{p^{2} e^{p t} + e^{p t}} + \frac{\sin{\left(t \right)}}{p^{2} e^{p t} + e^{p t}} & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
/        p                               
|      ------         for 2*|arg(p)| < pi
|           2                            
|      1 + p                             
|                                        
| oo                                     
<  /                                     
| |                                      
| |          -p*t                        
| |  cos(t)*e     dt       otherwise     
| |                                      
|/                                       
\0
{pp2+1for 2∣arg⁡(p)∣<π∫0∞e−ptcos⁡(t) dtotherwise\begin{cases} \frac{p}{p^{2} + 1} & \text{for}\: 2 \left|{\arg{\left(p \right)}}\right| < \pi \\\int\limits_{0}^{\infty} e^{- p t} \cos{\left(t \right)}\, dt & \text{otherwise} \end{cases} 
=
= 
/        p                               
|      ------         for 2*|arg(p)| < pi
|           2                            
|      1 + p                             
|                                        
| oo                                     
<  /                                     
| |                                      
| |          -p*t                        
| |  cos(t)*e     dt       otherwise     
| |                                      
|/                                       
\0
{pp2+1for 2∣arg⁡(p)∣<π∫0∞e−ptcos⁡(t) dtotherwise\begin{cases} \frac{p}{p^{2} + 1} & \text{for}\: 2 \left|{\arg{\left(p \right)}}\right| < \pi \\\int\limits_{0}^{\infty} e^{- p t} \cos{\left(t \right)}\, dt & \text{otherwise} \end{cases} 
Piecewise((p/(1 + p^2), 2*Abs(arg(p)) < pi), (Integral(cos(t)*exp(-p*t), (t, 0, oo)), True))

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

    © Sr Examen – Калькулятор