int х^(1/3)/(x^(1/3) - 1) dx = | x^(1/3) = t; x = t^3; dx = 3 * t^2 dt| =
= int t * 3 * t^2/(t - 1) dt = 3 * int t^3/(t - 1) dt = 3 * int (t^3 - 1 + 1)/(t - 1) dt =
= 3 * int (t^3 - 1)/(t - 1) dt + 3 * int dt/(t - 1) =
= 3 * int (t - 1) * (t^2 + t + 1)/(t - 1) dt + 3 * ln |t - 1| =
= 3 * int (t^2 + t + 1) dt + 3 * ln |t - 1| =
= 3 * (1/3 * t^3 + 1/2 * t^2 + t) + 3 * ln |t - 1| + C =
= t^3 + 3/2 * t^2 + 3 * t + 3 * ln |t - 1| + C = | t = x^(1/3) | =
= x + 3/2 * x^(2/3) + 3 * x^(1/3) + 3 * ln |x^(1/3) - 1| + C