Întrebare
Calculati prin metoda integrarii prin parti integrala din x lnx dx.
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[tex] \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 } \,=[/tex]
[tex]= \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=[/tex]
[tex]\frac{x^2}{2}lnx- \frac{x^2}{4}+C[/tex]
[tex]= \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=[/tex]
[tex]\frac{x^2}{2}lnx- \frac{x^2}{4}+C[/tex]