kill(all)$

van=facebook.com/LearningCalculus$

f(x,n,p):=log(x)^n/x^(p+1);

h1[p]:=integrate(f(x,1,p),x,1,inf)$
M:create_list(h1[p],p,1,12);
factor(M);

h2[p]:=integrate(f(x,2,p),x,1,inf)$
M:create_list(h2[p],p,1,12);
factor(M);

h3[p]:=integrate(f(x,3,p),x,1,inf)$
M:create_list(h3[p],p,1,12);
factor(M);