Anomalous integral 2 to positive infinity 1 / X (LNX) ^ k DX

Anomalous integral 2 to positive infinity 1 / X (LNX) ^ k DX

∫ 1 / X (LNX) ^ k DX = ∫ (LNX) ^ k dlnx, because 1 / xdx = dlnx if (K ≠ - 1) = (LNX) ^ (K + 1) / (K + 1) + C if (k = - 1) = ln (LNX) + C, the anomalous integral is = LIM (x → + ∞) (LNX) ^ (K + 1) / (K + 1) - (LN2) ^ (K + 1) / (K + 1) if K + 1 > 0, then the integral diverges if K + 1