<p>In this paper, we consider the inverse problem for determining the multi-factor source in the fractional diffusion equations from the knowledge of an integral type measurement. We first construct a second-type integral identity that combines the unknown sources and the integral type observation, and we establish the wellposedness of the inverse problem by using operator theories. More specifically, first, by virtue of the Mittag-Leffler functions, we use the eigenfunction expansion argument and the Neumann lemma to show that the operator equation locally admits a unique solution. Second, using the strong maximum principle and the Krein-Rutman theorem, we show the compactness of the operator in the integral equation, from which the wellposedness of the inverse problem is proved by the Fredholm alternative. Finally, an algorithm based on the Tikhonov regularization is proposed, and several numerical experiments are presented to show the accuracy and efficiency of the algorithm.</p>