Question

\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]

Answer 1

\[\text{ Let I }= \int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]

\[\text{ Also let  e}^x \times \frac{1}{x^2} = t \]

\[\text{ Diff  both  sides w . r . t x }\]

\[ e^x \times \frac{1}{x^2} + e^x \left( \frac{- 2}{x^3} \right) = \frac{dt}{dx}\]

\[ \Rightarrow e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx = dt\]

\[ \therefore \int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx = \int dt\]

\[ = t + C\]

\[ = \frac{e^x}{x^2} + C\]