What is the antiderivative of the function (g(x)-2)^2 if g(x)=x+e^x+2?

The antiderivative is the indefinite integral of the
function `(g(x)-2)^2 = (x + e^x + 2 - 2)^2 = (x + e^x)^2 = x^2 + 2xe^x +
e^(2x)`

We'll integrate both
sides:

`int (g(x)-2)^2dx = int x^2dx + 2int xe^xdx + int
e^(2x)dx` `int (g(x)-2)^2dx = (x^3)/3 + (e^(2x))/2 + 2int
xe^xdx`

`int udv = uv - int
vdu`

`` `u = x =gt du =
dx`

`` 

`dv = e^x =gt v =
e^x`

`int xe^xdx = xe^x - int e^x
dx`

`` `int xe^xdx = xe^x - e^x +
C`

Therefore, the requested antiderivative of
the function is:

`int
(g(x)-2)^2dx = (x^3)/3 + (e^(2x))/2 + 2xe^x - 2e^x + C`