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Solving integrals/ ye^(xy/2)

Integral of ye^(xy/2) dy

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |     x*y   
 |     ---   
 |      2    
 |  y*E    dy
 |           
/            
0
∫01exy2y dy\int\limits_{0}^{1} e^{\frac{x y}{2}} y\, dy 
Integral(y*E^((x*y)/2), (y, 0, 1))
The answer (Indefinite) [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                      |
                   \\                              /
∫exy2y dy=C+{(2xy−4)exy2x2for x2≠0y22otherwise\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}
Simplify
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
{(2x−4)ex2x2+4x2for x>−∞∧x<∞∧x≠012otherwise\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
{(2x−4)ex2x2+4x2for x>−∞∧x<∞∧x≠012otherwise\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.

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