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Solving integrals/ ysin(xy)

Integral of ysin(xy) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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

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

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