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Solving integrals/ y*sin((x*y)/2)

Integral of y*sin((x*y)/2) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
   2                
 ------             
   ____             
 \/ pi              
    /               
   |                
   |        /x*y\   
   |   y*sin|---| dx
   |        \ 2 /   
   |                
  /                 
  x                 
  -                 
  2
∫x22πysin⁡(xy2) dx\int\limits_{\frac{x}{2}}^{\frac{2}{\sqrt{\pi}}} y \sin{\left(\frac{x y}{2} \right)}\, dx 
Integral(y*sin((x*y)/2), (x, x/2, 2/sqrt(pi)))
The answer (Indefinite) [src] 
  /                      //     0       for y = 0\
 |                       ||                      |
 |      /x*y\            ||      /x*y\           |
 | y*sin|---| dx = C + y*|<-2*cos|---|           |
 |      \ 2 /            ||      \ 2 /           |
 |                       ||-----------  otherwise|
/                        \\     y                /
∫ysin⁡(xy2) dx=C+y({0for y=0−2cos⁡(xy2)yotherwise)\int y \sin{\left(\frac{x y}{2} \right)}\, dx = C + y \left(\begin{cases} 0 & \text{for}\: y = 0 \\- \frac{2 \cos{\left(\frac{x y}{2} \right)}}{y} & \text{otherwise} \end{cases}\right)
Simplify
The answer [src] 
/       /  y   \        /x*y\                                  
|- 2*cos|------| + 2*cos|---|  for And(y > -oo, y < oo, y != 0)
|       |  ____|        \ 4 /                                  
<       \\/ pi /                                               
|                                                              
|             0                           otherwise            
\
{−2cos⁡(yπ)+2cos⁡(xy4)for y>−∞∧y<∞∧y≠00otherwise\begin{cases} - 2 \cos{\left(\frac{y}{\sqrt{\pi}} \right)} + 2 \cos{\left(\frac{x y}{4} \right)} & \text{for}\: y > -\infty \wedge y < \infty \wedge y \neq 0 \\0 & \text{otherwise} \end{cases} 
=
= 
/       /  y   \        /x*y\                                  
|- 2*cos|------| + 2*cos|---|  for And(y > -oo, y < oo, y != 0)
|       |  ____|        \ 4 /                                  
<       \\/ pi /                                               
|                                                              
|             0                           otherwise            
\
{−2cos⁡(yπ)+2cos⁡(xy4)for y>−∞∧y<∞∧y≠00otherwise\begin{cases} - 2 \cos{\left(\frac{y}{\sqrt{\pi}} \right)} + 2 \cos{\left(\frac{x y}{4} \right)} & \text{for}\: y > -\infty \wedge y < \infty \wedge y \neq 0 \\0 & \text{otherwise} \end{cases} 
Piecewise((-2*cos(y/sqrt(pi)) + 2*cos(x*y/4), (y > -oo)∧(y < oo)∧(Ne(y, 0))), (0, True))

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

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