Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Integrate the rational functions 1 upon e raised to x

Q21 Integrate the rational functions \frac{1}{( e ^x-1)} [Hint : Put e ^x= t]

Answers (1)

best_answer

Given function \frac{1}{( e ^x-1)}

So, applying the hint: Putting e^x = t

Then e^x dx= dt

\int \frac{1}{( e ^x-1)}dx = \int\frac{1}{t-1}\times\frac{dt}{t} = \int \frac{1}{t(t-1)}dt

 

Partial fraction of above equation,

\frac{1}{t(t-1)} = \frac{A}{t}+\frac{B}{(t-1)}

1= A(t-1)+Bt                                            ..............(1)                            

Now, substituting t = 0\ and\ t = 1 in equation (1), we get

A = -1\ and\ B=1

\Rightarrow \frac{1}{t(t+1)} = -\frac{1}{t}+\frac{1}{t-1}

\implies \int \frac{1}{t(t-1)}dt = \log \left | \frac{t-1}{t} \right |+C

Now, back substituting the value of t,

= \log \left | \frac{e^x-1}{e^x} \right |+C

 

Posted by

Divya Prakash Singh

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 Chemistry Exam Analysis 2025: Paper 'moderately difficult' but well balanced
anam-khan

CBSE Class 12 board exam still once a year; 20 lakh expected to appear in 2026 from February 17
anam-khan

CBSE board exams twice a year from 2025-26; 2 subject groups, 'better of two marks' in draft policy

Latest Question