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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 16

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 16

Answers (1)

Answer:-\log|e^{-x}+2|+c

Hint: You must know about the integration rule of exponential function.

Given: \int \frac{1}{1+2e^{x}}dx

Solution: \int \frac{1}{1+2e^{x}}dx

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

=\int \frac{e^{-x}}{e^{-x}+2}dx                          [ multiply and divide by e^{x}]

Lett = e^{-x}+2   and differentiate both sides, \left [ \frac{d}{dx}e^{-x}= -e^{-x} \right ]

 dt = -e^{-x} dx

I=\int \frac{-dt}{t}

=-\log \left | t \right |+c

=-\log \left | e^{-x} +2\right |+c                                                                  \left [\int \frac{1}{x}dx=\log x+c \right ]

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