Question

integrala x² lnx dx =?

Answer 1

prin parti
u=lnx,du=$\frac{1}{x}dx$
dv=$x^{2} dx,v= \frac{x^3}{3}$
$\int\limits {x^2}lnx \, dx= \frac{x^3}{3}lnx- \int\limits{ \frac{x^3}{3} * \frac{1}{x} } \, dx= \\ \frac{x^3}{3}lnx- \int\limits { \frac{x^2}{3} } \, dx= \frac{x^3}{3}lnx - \frac{x^3}{9}+C= \\ \frac{x^3}{3}(lnx- \frac{1}{3} )+C$