integrala x^2*ln^2(x)
f=ln^2(x) =>f derivat = 2ln(x) totul pe x
g derivat = x^2 => g=1/3*x^3
faci cu derivarea prin parti
1/3*x^3*ln^2(x) - [tex] \int\ { \frac{2ln(x)}{x}* \frac{x^3}{3} } \, dx [/tex]
acul luam f=lnx f'=1/x
g'=x^2 g=1/3*x^3
(.......)-2/3*(1/3*(x^3)*ln(x)-[tex] \int { \frac{1}{x}* \frac{x^3}{3} } \, dx [/tex]
(......)-1/3 [tex]1/3* \int {x^2} \, dx =1/9*x^3[/tex]
