Integral involving exponential of a square matrix

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Hi, I am trying to evaluate an integral involving exponential of a square matrix and numerical evaluation would be fine. I am bit concerned that I may do something wrong as it involves exponential of matix.
I1 = exp^( - integral ([A_mo+ Alpha_m0 . G(t)] dt))
I2 = integral (I1. [G(t)-1] dt)
where G(t) is a Gaussian scalar. A_mo and Alpha_m0 are 6 x 6 matrices.
Attached .m file contains the structures if both A_mo and Alpha_m0. It also contains my attempt at calculating I1 and I2.
Regards, DK

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