# Haar measure and Integral

I am wondering whether the following integral over Haar measure has explicit form（edit: say $$U$$ is $$d\times d$$ unitary, orthogonal or symplectic matrix) $$\int dU [(U\otimes U^*)X(U^{+}\otimes U^T)]^{\otimes n}$$ where $$X$$ is a given $$d^2\times d^2$$ Hermitian matrix, $$U^{*}$$ is the element-by-element complex conjugation of $$U$$, $$U^{+}$$ is the Hermitian transpose of $$U$$, $$U^T$$ is the transpose of $$U$$, and $$n,d$$ are known integers.