I have a function:
and I would like to integrate it twice against x to obtain .
More precisely, I need to compute
which can also be written
However there are no symmetries that can be exploited. can have any positive real value.
Until now I have obtained a quite complicated expression for with explicit terms and two simple integrals which I can't figure out how to compute, namely :
Any idea to integrate this function ? I have not been lucky with variable changes...
PS: for those interested, it is an integration involved in the computation of the van der Waals interaction energy between two solid cubes of size a1 and a2 and separated by a distance d in the x direction...