The integrated backscatter communication (BackCom) and active communication (AC) scheme can improve wireless powered mobile edge computing (WPMEC) system performance in general single-user and multi-user scenarios. However, there is little research in the cooperation-assisted WPMEC scenario. In this paper, we consider a cooperation-assisted WPMEC system consisting of a source node (SN), a helper and a hybrid access point (HAP) integrated with MEC servers. An innovative user cooperation (UC) scheme with integrated BackCom and AC is proposed to enhance the system performance. As a relay, the helper can help the SN to transmit its computing tasks due to the poor communication link between the SN and the HAP. To be specific, we aim at maximizing the user energy efficiency (EE) by jointly optimizing backscatter reflection coefficient for BackCom, transmission power for AC, system time and tasks allocation while considering the minimum computation bits requirement, the channel capacity and energy constraints. Based on a fractional program, the EE maximization problem first is transformed to an equivalent one. Then, we exploit variable substitution and convex optimization to transform this non-convex problem into a convex problem. In addition, semi-closed form expressions of the optimal solution are deduced. An energy efficiency maximization algorithm is proposed to solve this problem. Simulation results demonstrate that the proposed scheme significantly improves the user EE than the existing schemes.