Integration by Parts in matrices

Question

Given Data in the question

1. We have a given equation based on matrices as follows

$\frac{\mathrm{d} R(s)_{3\times3}}{\mathrm{d} s}=R(s)_{3\times3}K(s)_{3\times3} \tag 1$

2. $\frac{\mathrm{d} R(s)_{3\times3}}{\mathrm{d} s},K(s)$ have zero determinant and $K(s)$ is skew symmetric matrix
3. $R(s)$ is a rotation matrix.(Determinant 1, orthogonal, etc )

Question

1. Can we write $\int R(s) \ ds$ using integration by parts rule?

   R.H.S can be any term which includes derivatives of $K(s),R(s)$ and integral of $K(s)$ as per convenience(but no integral must of the form of product of two variable matrices,looking for simplified form,means for example $\int R(s)_{3\times3}K(s)_{3\times3} \ ds $ has to be simplified) but it must not contain any $\int R(s) \ ds$ term. Basically I am trying to find $\int R(s) \ ds$ (L.H.S) from given relationship. Remember only $R(s)$ can be invertible rest are not