I'll try again to type correctly:

`int` x*`e^(x)` = `int` dy = Y

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

`int` x*`e^(x)` dx = `e^(x)`*(x - 1) + C

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

There are missing some integral signs and I'll re-write the answer again:

`int` x*`e^(x)` dx = `int` dy = Y

We'll integrate by parts using the formula:

`int` udv = uv - `int` vdu

Let u = x => du = dx

Let dv = dx => v =

`int` x* dx = x* - dx

`int` x*dx = x*- + C

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

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.**