Stuck trying to get a general solution for a separable differential equation

Hi, I have the following problem:

Consider the differential equation

$dy/dx=y^2+3y+2$

A) State whether the differential equation is linear and/or separable.

B) Obtain the general solution, expressing y explicitly as a function of x.
________

For A) I have that the equation is nonlinear, but it is separable.

And in B, I am stuck at the end (trying to express y as a function of x).

I got this, but I don't know what else to do.... thanks! (please, let me know if this is actually a general solution as well)

$dy/dx=1/(y^2+3y+2)^{-1}$

$dy(y^2+3y+2)^{-1}=dx$

$\int (y^2+3y+2)^{-1}dy=\int dx$

$\int 1/(y^2+3y+2)dy=\int dx$

$\int 1/(y+1)-\int 1/(y+2) dy=\int dx$

$ln|y+1|-ln|y+2|=x+C$

$ln|(y+1)/(y+2)|=x+C$

$(y+1)/(y+2)=e^{x+C}$

So that's where I am stuck (Angry)