Find y if dy/dx=xe^x?

To determine the primitive function Y, we'll have to
calculate the indefinite integral of the given function:

x*`e^(x)`dx = `int`dy = Y

We'll integrate by parts using
the formula:

udv = uv -
vdu

Let u = x => du =
dx

Let dv = `e^(x)` dx => v =
`e^(x)`

x*`e^(x)` dx = x*`e^(x)` - `int` `e^(x)`
dx

x*`e^(x)`= x*`e^(x)`- `e^(x)`+
C

The requested primitive function
is Y = (x-1)*`e^(x)` + C.