Question

∫1 2dx/(x-1)^(2⁄3) la integral impropia los límites son de 1 hasta 2 de dx/(x-1) elevado a 2/3

Answer 1

$\displaystyle I=\int\limits_{1}^{2}\dfrac{1}{(x-1)^{2/3}}dx\\ \\ \\ I=\lim\limits_{a\to1^+}\int\limits_{a}^{2}\dfrac{1}{(x-1)^{2/3}}dx\\ \\ \\ I=\lim\limits_{a\to1^+} \left.\left[3(x-1)^{1/3}\right]\right|_{a}^{2}\\\\\\ I=3\lim\limits_{a\to1^+} 1-(a-1)^{1/3}\\\\\\ \boxed{I=3}$