Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 16 Maths Textbook Solution.

Answers (1)

Answer:

$x-\log \left|e^{x}+1\right|+c$

Given:

$\int \frac{1}{e^{x}+1} d x$

Hint:

Do integration by separation.

Solution:

$\int \frac{1}{e^{x}+1} d x$

$=\int \frac{\left(e^{x}+1\right)\left(-e^{x}\right)}{e^{x}+1} d x$

$=\int d x-\int \frac{e^{x}}{e^{x}+1} d x$

$now, let e^{x}+1=u$

Differentiate it with respect to x

$\frac{d u}{d x}=e^{x}$

$d u=e^{x} d x$

now,

$I=\int d x-\int \frac{1}{u} d u$

$=x-\log |u|+c$

$=x-\log \left|e^{x}+1\right|+c \quad\left(\because u=e^{x}+1\right)$

Posted by

infoexpert21

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 Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th

anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question