I tried to integrate simpler expression:
f:=1/((1+exp(x)))^0.333;
Result takes some screens and contains logs and arctans but it works!
And now I am still waiting for intergation of your formula...
May be you can simplify or reorganize your expression.
Update.
Not enough memory (Kernel error) - I have only 8 Gb. May be it needs more memory and time?
Maple 2016.