What is the analytic closed form expression of
$\int e^{A_1+A_2s} \ ds \tag 1$
where A and B are constant skew symmetric matrices
NB
$A_1=\left( \begin{array}{ccc} 0 & -c_0 & b_0 \\ c_0 & 0 & -a_0 \\ -b_0 & a_0 & 0 \\ \end{array} \right) \tag 2$
$A_2=\left( \begin{array}{ccc} 0 & -c_1 & b_1 \\ c_1 & 0 & -a_1 \\ -b_1 & a_1 & 0 \\ \end{array} \right) \tag 3$ All $a_i,b_i,c_i$ ($i= 0,1$) are constants. Only s is the variable
$A_1+A_2s$ and $ (A_1+A_2s)^{'} $ (derivative) are not commutative
I tried to use expression for matrix exponent in skew symmetric matrices using the formula shown below
Please click here(page 1 right bottom in the pdf link) for reference source . But the issue is this form is very tough to integrate