I have a problem where I need to evaluate $D=\int_a^be^{b(s)^T(c+Au)}ds $ where $b(s)$ is the B-spline. I know the Laplace method but I don't think I can use it here since it's the exponent of B-spline and $(c+Au)$ is not large. Can anyone help me how to evaluate or at least what methods or rules to apply for this kind of equation? The way I can think is
$D=\int_a^be^{b(s)^T(c+Au)}ds $
$=>D=\dfrac{e^{z(s)}}{(c+Au)\dfrac{\partial b(s)}{\partial s}}$
where, $b(t)= {[b_1(t),...,b_p(t)]}$ be a spline basis,
$c$ is a p-dimensional coefficient vector, $A$ is a lower-traingular p*p matrix
and $u \sim N(0,I_p)$.
Can anyone please at least tell either it's correct or not.