Use integration by parts to establish the reduction formula: integral (ln x)^n dx = x(ln x)^n - n integral (ln x)^n-1 dx|: To begin the integration by parts, let u =| and dv =| dx. Evaluating du = | dx| and v = | leads immediately to the above reduction formula. Now apply the reduction formula to the problem: integral (ln x)^6 dx|. Getting the final result would be tedious, requiring 6| applications of the reduction formula. So for simplicity just give the result of applying the reduction formula one time. Integral (ln x)^6 dx| is simplified to:.