Let x1 x2 frac14 xn denote the elements of a gaussian

Question

Let X₁, X₂, ¼, X_n denote the elements of a Gaussian vector X. The X_i are independent with mean mi and variance , i = 1, 2, ¼, n. Show that the differential entropy of the vector X is given by

where e is the base of the natural logarithm.What does h(X) reduce to if the variances are all equal?