Вычислить интеграл (x^2+1)ln xdx

[tex] \int\ {(x^2 + 1)lnx} \, dx = по частям = [u = lnx, dv = (x^2 + 1)dx, =\ \textgreater \ [/tex] [tex]du = \frac{1}{x}dx, v = \frac{x^3}{3} + x] = ( \frac{x^3}{3} + x) lnx - \int\ { ( \frac{x^3}{3} + x) \frac{1}{x}} \, dx = ( \frac{x^3}{3} + x) lnx - [/tex][tex] \frac{x^3}{3} - x + C[/tex]