How would I use separation of variables to solve the initial value problem?

Question

dy/dx = (y +5)(x+2)
I multiply both sides by dx so: dy= (y+5)(x+2)dx
Then I get variables on the same sides:: dy/(y+5)= (x+2)dx
Then I have to take integrals of both sides but this is where I get stuck. Can someone show me the rest? Thanks.

Answer 1

what is wrong with

ln(y+5)=1/2 (x+2)^2 +C

check

1/(y+5)dy=(x+2)dx
dy/dx=(x+2)(y+5)