Ito gives us $$dW = \dfrac{dW}{dX} dX + \left(\frac{dW}{dt} + \frac{1}{2} \frac{d^2W}{dX^2}\right) \, dt$$
We have a function $W(t) = 1 + t + E^{X(t)}$. My text book says that $$dW = e^{X(t)} \, dX + (1+e^{X(t)}) \, dt$$
Am I correct in asserting that the factor $\dfrac{1}{2}$ has been forgotten in front of the second $e^{X(t)}$?