Rules for integrands of the form(((c+d x))^m) (((a+b Sech[e+f x]))^n)

N:  ∫(u^m)((Sech[v])^n)dx  when  u==c+d x ∧ v==a+b x

Derivation: Algebraic normalization

Rule: If  u==c+d x ∧ v==a+b x, then

∫(u^m)((Sech[v])^n)dx  ⟶  ∫(((c+d x))^m) ((Sech[a+b x])^n)dx

Program code:

Int[u_^m_.*Sech[v_]^n_.,x_Symbol] :=
  Int[ExpandToSum[u,x]^m*Sech[ExpandToSum[v,x]]^n,x] /;
FreeQ[{m,n},x] && LinearQ[{u,v},x] && Not[LinearMatchQ[{u,v},x]]

Int[u_^m_.*Csch[v_]^n_.,x_Symbol] :=
  Int[ExpandToSum[u,x]^m*Csch[ExpandToSum[v,x]]^n,x] /;
FreeQ[{m,n},x] && LinearQ[{u,v},x] && Not[LinearMatchQ[{u,v},x]]