Integrate[x^(s-1-Log[2]/Log[3])*Log[Abs[y+2-x]],x]

Integrate[x^(s-1-Log[2]/Log[3])*Log[Abs[y+2-x]],{x,0,Infinity}]

mel6[s_,y_]:=Integrate[x^(s-1-Log[2]/Log[3])*Log[Abs[y+2-x]],{x,1,Infinity}];

mel6[0,0]

mel6[0,0]

Integrate[x^(-Log[2]/Log[3]-1-2*I*Pi*n/Log[3])*Log[2+y-x],x]

mel7[a_]:=Integrate[x^(-Log[2]/Log[3]-1-2*I*Pi*1/Log[3])*Log[2+0.6-x],{x,a,1}]

Clear[mel7];