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

Integral of y*sin(x*y*z) dx

Limits of integration:

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The solution

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

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

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