Solving linear first order differential equation with hard integral I'm try to solve this differential equation: $y'=x-1+xy-y$
After rearranging it I can see that is a linear differential equation:
$$y' + (1-x)y = x-1$$
So the integrating factor is $l(x) = e^{\int(1-x) dx} = e^{(1-x)x}$
That leaves me with an integral that I can't solve... I tried to solve it in Wolfram but the result is nothing I ever done before in the classes so I'm wondering if I made some mistake...
This is the integral:
$$ye^{(1-x)x} = \int (x-1)e^{(1-x)x} dx$$

A much easier way without an integrating factor:
$y′=x−1+xy−y$
$y′=x-1+y(x-1)$
$y′=(x-1)(1+y)$
$\frac{dy}{(1+y)} = (x-1)dx$
$ln|1+y| = x^2/2 -x + C$
And you can do the rest
