Question

E ∫ ln^2(x)/x помогите 1

Answer 1

$\int\limits^{e}_1 \frac{ln^2x}{x} \, dx = \int\limits^{e}_1 \, ln^2x\cdot \frac{dx}{x}= \int\limits^{e}_1 (lnx)^2 \cdot d(lnx)=[\int u^2\, du=\frac{u^3}{3}+C]=\\\\= \frac{ln^3x}{3} \Big |_1^{e}=\frac{ln^3e}{3}-\frac{ln^31}{3}=\frac{1}{3}$