In task 2 and 5 we are supposed to derive expressions for \( s(T) \) and \( \rho c^2(T) \). These are written in a compact form in the end, but initially written with the full expressions. Do we have to arrive at the initial expressions at first, and then write the solutions in terms of \( \mathcal{S}(x) \) and \( \mathcal{E}(x) \), or can we just go straight to the final expressions? I think I will save a lot of time/space by not rewriting the expressions to obtain the initial expressions at first