I am trying to use Maple to discretize a model by solving an integral analytically. In my textbook the problem is solved by using Maple and is according to them "These calculations are quite straightforward to compute with Maple".

In my textbook there is an example where the non-linear system with state vector x(t) = [x1(t), x2(t), v(t), h(t), w(t)]' is described as

dx/dt=[v*cos(h), v*sin(h), 0, w, 0]'=a(x(t)).

To discretize this model the sampling formula x(t+T) = x(t) + int(a(x(tau)), tau=t..t+T) is used

Firstly, we can integrate the expressions row by row, the first row would then be

x1(t+T)=x1(t)+int(v(tau)*cos(h(tau)), tau=t..t+T).

The result when the sampling formula is applied to the first row in the example is

x1(t+T)=x1(t)+2v(t)/w(t)*sin(w(t)T/2)*cos(h(t)+w(t)T/2)

I have tried using int() and dsolve() but have only managed to get results that involve integrals. I would appreciate if someone more experienced could help me with this and maybe shed some light on if it actually is possible to do this?