Mariusz (and Marvin, too):
I don't know yet if I can have access to MATHEMATICA 14.2.0, so that I cannot check your results, but I think your result for the integral involving the first power of Q cannot be correct. It is different from the expected formula
(Sqrt[π/D]/D/12)*((2*Sqrt[D*t/π])*(2*D*t-x^2)*Exp[-(x^2)/(4*D*t)]+(x^3)*Erfc[x/Sqrt[4*D*t]])
and it does not agree with the special case of x=0, in which it should be equal to
t^(3/2)/3
I am sure that especially the latter formula is correct, because it has one more independent verification.
I also suspect that your formulae for the integral with Q squared (and further integrals) are not correct, as from my knowledge this integral does not have an analytical representation.
I think the reason can be that you changed my variables xx to x and tt to t in the formula for Q, but not in the declaration Q[xx,tt]? If this is not the reason, then there must be a bug in MATHEMATICA.
Leslaw
