Let I_n(x)\equal{}\int_1^x (\ln t)^ndt\ (x>0) for n\equal{}1,\ 2,\ 3,\ \cdots.
(1) Prove by mathematical induction that In(x) is expressed by I_n(x)\equal{}xf_n(\ln x)\plus{}C_n\ (n\geq 1) in terms of some polynomial fn(y) with degree n and some constant number Cn.
(2) Express the constant term of fn(y) interms of n. calculusintegrationlogarithmsinductionalgebrapolynomialcalculus computations