Maple will not evaluate this Laplace integral

Question

Maple is returning a limit in my answer and will not apply the limit. I am specifically trying to evaluate the Laplace Integral of the function f(t) = cos(omega*t)^2

Maple code sample

I use the laplace() command to confirm my answer. If Maple would apply the limit, then I would get the expected answer.

What is happening? How can I force Maple to evaluate the limit?

Answer 1

inttrans[laplace](cos(w*t)^2,t,s);

   (s^2+2*w^2)/(s^2+4*w^2)/s

int(exp(-s*t)*cos(w*t)^2,t=0..infinity) 
  assuming s>0;

   (s^2+2*w^2)/(s^2+4*w^2)/s

int(exp(-s*t)*cos(w*t)^2,t=0..infinity)
  assuming s<0;

         undefined