Integrable modules for loop affine-Virasoro algebra

In this paper we classify the irreducible integrable modules for the loop affine-Virasoro algebra $(( \overset{\circ}{\mathfrak{g}} \otimes $\mathbb{C}$[t, t^{-1}] \oplus $\mathbb{C}$ K) \rtimes $\text{Vir}$) \otimes A$,where$A$ is a finitely generated commutative associative algebra with unity.