ok so i have the differential equation:
dx/dt = ((x-1)^2)*(t+1)
this is separable and separation of variables gives
integral ( dx/((x-1)^2)) = integral (t+1) dt
im told the correct answer is..
-1 / (x-1) = ((t+1)^2)/2 + c
but am wondering, why cant i go back to the differential equation and integrate the RHS as:
(t^2)/2 + t + c
why is (t+1) integrated together... why not integrate t first... and then 1... ? surely thats more simple??