Question

integrare prin părți din 1/x ln x dx = ?
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Answer 1

$\int {\frac{1}{x} lnx} \, dx = \int {\ (lnx)' lnx} \, dx = ln^2x - \int {\frac{1}{x} lnx} \, dx$

Adaugam integrala din 1/x lnx dx in dreapta si in stanga :

$2\int {\frac{1}{x} lnx} \, dx = ln^2x\\\\\int {\frac{1}{x} lnx} \, dx = \frac{ln^2x}{2}$