Răspunsuri

2014-10-20T19:17:56+03:00
Presupun ca stim \int\ln x\ dx=x(\ln x-1)  .

Atunci integrala ceruta se scrie, folosind integrarea prin parti:

=\int\ln x\ln x\ dx=\\ \\ =\int[x(\ln x-1)]'\ln x\ dx=\\ \\ \\ =x(\ln x-1)\ln x-\int x(\ln x-1)\cdot \frac{1}{x}=\\ \\ \\ =x(\ln x-1)\ln x-\int(\ln x-1)\ dx=\\ \\ \\ =x(\ln x-1)\ln x-x(\ln x-1)+x+C=\\ \\ \\ =x[(\ln x-1)^2+1]+C
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