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प्रश्न
\[\int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
योग
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उत्तर
\[\text{ Let I }= \int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx\]
\[\text{ Also let e}^x \times \frac{1}{x^2} = t \]
\[\text{ Diff both sides w . r . t x }\]
\[ e^x \times \frac{1}{x^2} + e^x \left( \frac{- 2}{x^3} \right) = \frac{dt}{dx}\]
\[ \Rightarrow e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx = dt\]
\[ \therefore \int e^x \left( \frac{1}{x^2} - \frac{2}{x^3} \right) dx = \int dt\]
\[ = t + C\]
\[ = \frac{e^x}{x^2} + C\]
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