Question

Вычислить интеграл {x^2ln xdx

Answer 1

{x^2 ln(x) dx = ...

Интегрирование по частям: {u dv = u v - {v du

u = ln(x), du = d ln(x) = dx/x

dv = x^2 dx, v = { x^2 dx = (x^3)/3

... = x^3 ln(x) /3 - (1/3) {x^2dx = (x^3)/3 [ ln(x) - 1/3 ] + Const