class 12 maths integrals

${e^x}\left( {\cfrac{1}{x} - \cfrac{1}{{{x^2}}}} \right)$

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📘 Integrals NCERT,ex.7.6,Q.19,Page 328 SA

${e^x}\left( {\cfrac{1}{x} - \cfrac{1}{{{x^2}}}} \right)$

Official Solution

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Let $I = \int {{e^x}\left( {\cfrac{1}{x} - \cfrac{1}{{{x^2}}}} \right)dx} = \int {{e^x}\left( {\cfrac{1}{x} + \left( {\cfrac{d}{{dx}}\left( {\cfrac{1}{x}} \right)} \right)} \right)} dx$

$= \left[ {{e^x} \times \cfrac{1}{x} + C} \right]$

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