why the ans from the tabular method is different from the by part method ? why the ans from for each term of tabular method is more than the by part method by 1/2 ?

the first terms of the ans from the tabular method is(x^3)(cosh 2 x) , but not 1/2(x^3)(sinh 2 x) ... and so on....
but the final ans below the tabular method there give 1/2(x^3)(sinh 2 x) , tat's weird