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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 33

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Answer: \frac{e^{x}}{x}+c

Hints: You must know about the integral rule of exponential functions

Given: \int e^{x}\left ( \frac{1}{x}-\frac{1}{x^{2}} \right )dx


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

It is of form

\int e^{x}f\left ( x \right )+{f}'\left ( x \right )dx=e^{x}.f\left ( x \right )+c

Put f\left ( x\right )=\frac{1}{x} and differentiate both sides,   

{f}'\left ( x\right )=\frac{-1}{x^{2}}


\int e^{x}\left ( \frac{1}{x}-\frac{1}{x^{2}} \right )dx=\frac{e^{x}}{x}+c

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