Question

Найдите:
$\int\limits^e_1 {\frac{ln^3x}{x}} \, dx$

Answer 1

$\int \limits ^{e} _{1} \frac{ {ln}^{3}x }{x} dx = \int \limits ^{e} _{1} ln^{3}x \: d( lnx)= \frac{ {ln}^{4}x }{4} \: |^e_1 = \frac{1}{4} - 0 = 0.25$