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Integral of x*y*e^(x*y)*dx dx

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The solution

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

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