xln-x-x-ln-3-x-dx-

Question Number 61874 by aliesam last updated on 10/Jun/19

\int \frac{x l n (x) - x}{{l n}^{3} (x)} d x

Commented by Prithwish sen last updated on 10/Jun/19

\int [\frac{x}{{[\ln (x)]}^{2}} - \frac{x}{{[\ln (x)]}^{3}}] dx

applying by parts

= \frac{x^{2}}{2 {[\ln (x)]}^{2}} + \int \frac{x}{{[\ln (x)]}^{3}} dx - \int \frac{x}{{[\ln (x)]}^{3}} + C

= \frac{x^{2}}{2 {[\ln (x)]}^{2}} + C