Question

Sa se calculeze integralele nedefinite,folosind formula de integrare prin parti:
Integrala x*2 ln x dx,x>0;
Integrala xe*-x dx,x>0.

Answer 1

$\int\limits { x^{2} lnx} \, dx = \frac{x^3}{3}lnx- \int\limit { \frac{x^3}{3}* \frac{1}{x} } \, dx=$
$= \frac{x^3}{3}lnx- \frac{1}{3} \int\limits { x^{2} } \, dx= \frac{x^3}{3}lnx- \frac{x^3}{9}+C$