Question

integral de e^1/x / x^2

Answer 1

$\textbf{Resolveremos por substitui\c{c}\~ao u.du:}\\\\ \mathrm{u=\dfrac{1}{x}\ \ \| \ \ \dfrac{du}{dx}=(x^{-1})'=-\dfrac{1}{x^2}\ \to\ du=-\dfrac{1}{x^2}.dx}\\\\ \mathrm{\int{e^{\frac{1}{x}}}\dfrac{1}{x^2}\ dx=\int -e^u\ du=-\int e^u\ du=-e^u}\\\\ \mathrm{*\ Como\ u=\dfrac{1}{x}\ \to\ \boxed{\mathbf{\int e^{\frac{1}{x}}\dfrac{1}{x^2}\ dx=-e^{\frac{1}{x}}+C}}}}$