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Integral of ye^(yx/2) dy

Limits of integration:

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Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |     y*x   
 |     ---   
 |      2    
 |  y*E    dy
 |           
/            
0            
$$\int\limits_{0}^{1} e^{\frac{x y}{2}} y\, dy$$
Integral(y*E^((y*x)/2), (y, 0, 1))
The answer (Indefinite) [src]
                   //              y*x             \
  /                ||              ---             |
 |                 ||               2              |
 |    y*x          ||(-4 + 2*x*y)*e          2     |
 |    ---          ||-----------------  for x  != 0|
 |     2           ||         2                    |
 | y*E    dy = C + |<        x                     |
 |                 ||                              |
/                  ||        2                     |
                   ||       y                      |
                   ||       --           otherwise |
                   ||       2                      |
                   \\                              /
$$\int e^{\frac{x y}{2}} y\, dy = C + \begin{cases} \frac{\left(2 x y - 4\right) e^{\frac{x y}{2}}}{x^{2}} & \text{for}\: x^{2} \neq 0 \\\frac{y^{2}}{2} & \text{otherwise} \end{cases}$$
The answer [src]
/                 x                                  
|                 -                                  
|                 2                                  
|4    (-4 + 2*x)*e                                   
<-- + -------------  for And(x > -oo, x < oo, x != 0)
| 2          2                                       
|x          x                                        
|                                                    
\       1/2                     otherwise            
$$\begin{cases} \frac{\left(2 x - 4\right) e^{\frac{x}{2}}}{x^{2}} + \frac{4}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$
=
=
/                 x                                  
|                 -                                  
|                 2                                  
|4    (-4 + 2*x)*e                                   
<-- + -------------  for And(x > -oo, x < oo, x != 0)
| 2          2                                       
|x          x                                        
|                                                    
\       1/2                     otherwise            
$$\begin{cases} \frac{\left(2 x - 4\right) e^{\frac{x}{2}}}{x^{2}} + \frac{4}{x^{2}} & \text{for}\: x > -\infty \wedge x < \infty \wedge x \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$
Piecewise((4/x^2 + (-4 + 2*x)*exp(x/2)/x^2, (x > -oo)∧(x < oo)∧(Ne(x, 0))), (1/2, True))

    Use the examples entering the upper and lower limits of integration.