Question

Digite o valor da integral
me ajudem :)

Answer 1

Explicação passo-a-passo:

Integral Definido

Dado o integral $\displaystyle\int\limits^{e/3}_{1/3}\dfrac{6\ln(3x)}{x}dx$

Seja $I~=~\displaystyle\int\limits^{e/3}_{1/3}\dfrac{6\ln(3x)}{x}dx$

$I~=~2\displaystyle\int\limits^{e/3}_{1/3}\ln(3x)d\left[\ln(3x)\right]$

$I~=~ \ln^2(3x)\Big|^{e/3}_{1/3}=\ln^2\left(3*\dfrac{e}{3}\right)-\ln^2\left(3*\dfrac{1}{3}\right)$

$I~=~\ln^2(e)-\ln^2(1)=1-0$

$I~=~\boxed{ 1 }$