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

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

Answers (1)

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

Solution:

\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}}

Thus,

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

Posted by

infoexpert27

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