Explicație pas cu pas:
[tex]\int_{1}^{e} {e}^{ ln(y) } ln(y)dy = \int_{1}^{e} y ln(y)dy = \\ =( \frac{ {y}^{2} (ln(y) }{2})_{1}^{e} - \int_{1}^{e} \frac{y}{2}dy \\ = ( \frac{ {y}^{2} (ln(y) }{2} - \frac{ {y}^{2} }{4} )_{1}^{e} \\ = ( \frac{ {y}^{2}( 2(ln(y) - 1}{4})_{1}^{e} \\ = \frac{ {e}^{2} + 1}{4} [/tex]
