The capacity region of the cooperative two-user Multiple Access Channel (MAC) in Gaussian noise is determined to within a constant gap for both the Full-Duplex (FD) and Half-Duplex (HD) case. The main contributions are: (a) for both FD and HD: unilateral cooperation suffices to achieve capacity to within a constant gap where only the user with the strongest link to the destination needs to engage in cooperation, (b) for both FD and HD: backward joint decoding is not necessary to achieve capacity to within a constant gap, and (c) for HD: time sharing between the case where the two users do not cooperate and the case where the user with the strongest link to the destination acts as pure relay for the other user suffices to achieve capacity to within a constant gap. These findings show that simple achievable strategies are approximately optimal for all channel parameters with interesting implications for practical cooperative schemes.