int (x * (ln x)^2) dx = int (ln x)^2 d(1/2 * x^2) = 1/2 * int (ln x)^2 d(x^2) =
= 1/2 * (ln x)^2 * x^2 - 1/2 * int x^2 d((ln x)^2) = 1/2 * (ln x)^2 * x^2 - 1/2 * int x^2 * ((ln x)^2)' dx =
= 1/2 * (ln x)^2 * x^2 - 1/2 * int x^2 * 2 * ln x * 1/x dx = 1/2 * (ln x)^2 * x^2 - int x * ln x dx =
= 1/2 * (ln x)^2 * x^2 - int ln x d(1/2 * x^2) = 1/2 * (ln x)^2 * x^2 - 1/2 * int ln x d(x^2) =
= 1/2 * (ln x)^2 * x^2 - 1/2 * ln x * x^2 + 1/2 * int x^2 d(ln x) =
= 1/2 * (ln x)^2 * x^2 - 1/2 * ln x * x^2 + 1/2 * int x^2 * 1/x dx =
= 1/2 * (ln x)^2 * x^2 - 1/2 * ln x * x^2 + 1/2 * int x dx =
= 1/2 * (ln x)^2 * x^2 - 1/2 * ln x * x^2 + 1/2 * 1/2 * x^2 + C =
= 1/2 * (ln x)^2 * x^2 - 1/2 * ln x * x^2 + 1/4 * x^2 + C = 1/4 * x^2 * (2 * (ln x)^2 - 2 * ln x + 1) + C