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Solving integrals/ xe^(xy)

Integral of xe^(xy) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |     x*y   
 |  x*e    dx
 |           
/            
0
∫01xexy dx\int\limits_{0}^{1} x e^{x y}\, dx 
Integral(x*E^(x*y), (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*e    dx = C - |<|----  for y  != 0           | + x*|
(x y−1) ex yy2{{\left(x\,y-1\right)\,e^{x\,y}}\over{y^2}}
Simplify
The answer [src] 
/               y                                  
|1    (-1 + y)*e                                   
|-- + -----------  for And(y > -oo, y < oo, y != 0)
< 2         2                                      
|y         y                                       
|                                                  
\      1/2                    otherwise
(y−1) eyy2+1y2{{\left(y-1\right)\,e^{y}}\over{y^2}}+{{1}\over{y^2}} 
=
= 
/               y                                  
|1    (-1 + y)*e                                   
|-- + -----------  for And(y > -oo, y < oo, y != 0)
< 2         2                                      
|y         y                                       
|                                                  
\      1/2                    otherwise
{(y−1)eyy2+1y2for y>−∞∧y<∞∧y≠012otherwise\begin{cases} \frac{\left(y - 1\right) e^{y}}{y^{2}} + \frac{1}{y^{2}} & \text{for}\: y > -\infty \wedge y < \infty \wedge y \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}
Simplify

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

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