Question

Calculati prin metoda integrarii prin parti integrala din x lnx dx.

Answer 1

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Answer 2

$\int\limits {x*lnx} \, dx = \int\limits (\frac{x^2}{2})' lnx {x} \, dx = \frac{x^2}{2}lnx- \int\limits { \frac{x^2}{2}* { \frac{1}{x} } \, dx } \,=$
$= \frac{x^2}{2}lnx- \frac{1}{2} \int\limits { \frac{x^2}{x} } \, dx = \frac{x^2}{2}lnx- \frac{1}{2} \int\limits {x} \, dx = \frac{x^2}{2}lnx- \frac{1}{2} * \frac{x^2}{2}+C=$
$\frac{x^2}{2}lnx- \frac{x^2}{4}+C$