The answer could be nicer, but try setting integrate_use_rootsof : true;

(%i14) integrate(1/((x-3)^4+1/2),x), integrate_use_rootsof : true;

(%o14) 2*'lsum(log(x-%r535)/(8*%r535^3-72*%r535^2+216*%r535-216),%r535,

rootsof(2*x^4-24*x^3+108*x^2-216*x+163))