Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

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

Answers (1)

best_answer

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 $e^{x}$ ]

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

$dt = -e^{-x} dx$

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

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

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

Posted by

infoexpert27

View full answer

Crack CUET with india's "Best Teachers"

HD Video Lectures
Unlimited Mock Tests
Faculty Support

cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE extends single girl child scholarship registration deadline till November 20

anam-khan

CBSE reminds schools to submit registration data of Class 9, 11 students by October 16

anam-khan

CBSE reopens online portal for submission of LOC for Class 10, 12 board exams 2026; submit forms by Oct 8

Latest Question