Dear Alejandro,

thank you for your answer. Can I the automatic simplifcation in order to get my desired result?

Of course I could use a workaround e.g. substituting u0(s)*u0(s) by a(s)*b(s), to the inverse Laplace transform and then resubstitute but I would like to avoid this.

@Carl Love  Thank you very much. Is there a possibility to get a step by step solution in Maple besides the ShowSolution command (which seems to work only for Calculus1 problems)?

@Carl Love 

Thanks for your answer, unfortunately ShowSolution does not seem to work with int.

Is there any possibility to see the step by step solution of this integral?

sorry, the correct link with exactly the same exression is this one:

http://www.wolframalpha.com/input/?i=Int%28sin%28k*%28t-tau%29%29*sin%28k*tau%29%2C+tau+%3D+0+..+t%29