Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 15

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 15

Answers (1)

best_answer

Answer:-\log|1+e^{-x}|+c

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

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

Solution:

\begin{aligned} &\int \frac{1}{1+e^{x}} d x \\ &=\int \frac{e^{-x}}{e^{-x}\left(1+e^{x}\right)} d x \quad\quad\quad\quad\quad\quad\quad\quad\left [ multiply\: and \: divide\: by \: e^{x} \right ]\\ &=\int \frac{e^{-x}}{1+e^{-x}} d x \end{aligned}

Let e^{-x}+1=t                                                                              \left [ \frac{d}{dx}e^{-x}= -e^{-x} \right ]

\begin{aligned} &-\mathrm{e}^{-x} \mathrm{~d} \mathrm{x}=\mathrm{dt} \\ &I=\int \frac{-d t}{t} \\ &=-\log |t|+c \\ &=-\log \left|e^{-x}+1\right|+c\quad\quad\quad\quad\quad\quad \quad\left[\int \frac{1}{x} d x=\log x+c\right] \end{aligned}

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 12th result 2025 sees more in compartment, JNVs on top, perfect-scorers in minor subjects
anam-khan

Low score in CBSE results? Courses, career options after 12th open to you
anam-khan

CBSE class 10, 12 results: West Bengal CM Mamata Banerjee congratulates successful candidates

Latest Question