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Integral de (ye^(xy/2)) dy

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
 log(3)         
    /           
   |            
   |      x*y   
   |      ---   
   |       2    
   |   y*E    dy
   |            
  /             
log(2)          
$$\int\limits_{\log{\left(2 \right)}}^{\log{\left(3 \right)}} e^{\frac{x y}{2}} y\, dy$$
Integral(y*E^((x*y)/2), (y, log(2), log(3)))
Respuesta (Indefinida) [src]
                   //              x*y             \
  /                ||              ---             |
 |                 ||               2              |
 |    x*y          ||(-4 + 2*x*y)*e          2     |
 |    ---          ||-----------------  for x  != 0|
 |     2           ||         2                    |
 | y*E    dy = C + |<        x                     |
 |                 ||                              |
/                  ||        2                     |
                   ||       y                      |
                   ||       --           otherwise |
                   ||       2                      |
                   \\                              /
$$\int e^{\frac{x y}{2}} y\, dy = C + \begin{cases} \frac{\left(2 x y - 4\right) e^{\frac{x y}{2}}}{x^{2}} & \text{for}\: x^{2} \neq 0 \\\frac{y^{2}}{2} & \text{otherwise} \end{cases}$$
Respuesta [src]
/                   x*log(3)                      x*log(2)                                  
|                   --------                      --------                                  
|                      2                             2                                      
|(-4 + 2*x*log(3))*e           (-4 + 2*x*log(2))*e                                          
|--------------------------- - ---------------------------  for And(x > -oo, x < oo, x != 0)
|              2                             2                                              
<             x                             x                                               
|                                                                                           
|                       2         2                                                         
|                    log (3)   log (2)                                                      
|                    ------- - -------                                 otherwise            
|                       2         2                                                         
\                                                                                           
$$\begin{cases} - \frac{\left(2 x \log{\left(2 \right)} - 4\right) e^{\frac{x \log{\left(2 \right)}}{2}}}{x^{2}} + \frac{\left(2 x \log{\left(3 \right)} - 4\right) e^{\frac{x \log{\left(3 \right)}}{2}}}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\- \frac{\log{\left(2 \right)}^{2}}{2} + \frac{\log{\left(3 \right)}^{2}}{2} & \text{otherwise} \end{cases}$$
=
=
/                   x*log(3)                      x*log(2)                                  
|                   --------                      --------                                  
|                      2                             2                                      
|(-4 + 2*x*log(3))*e           (-4 + 2*x*log(2))*e                                          
|--------------------------- - ---------------------------  for And(x > -oo, x < oo, x != 0)
|              2                             2                                              
<             x                             x                                               
|                                                                                           
|                       2         2                                                         
|                    log (3)   log (2)                                                      
|                    ------- - -------                                 otherwise            
|                       2         2                                                         
\                                                                                           
$$\begin{cases} - \frac{\left(2 x \log{\left(2 \right)} - 4\right) e^{\frac{x \log{\left(2 \right)}}{2}}}{x^{2}} + \frac{\left(2 x \log{\left(3 \right)} - 4\right) e^{\frac{x \log{\left(3 \right)}}{2}}}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\- \frac{\log{\left(2 \right)}^{2}}{2} + \frac{\log{\left(3 \right)}^{2}}{2} & \text{otherwise} \end{cases}$$
Piecewise(((-4 + 2*x*log(3))*exp(x*log(3)/2)/x^2 - (-4 + 2*x*log(2))*exp(x*log(2)/2)/x^2, (x > -oo)∧(x < oo)∧(Ne(x, 0))), (log(3)^2/2 - log(2)^2/2, True))

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