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 x/ x+ 1

Q1  Integrate the rational functions \frac{x }{( x +1)( x+2)}

Answers (1)

best_answer

Given function \frac{x }{( x +1)( x+2)}

Partial function of this function:

\frac{x }{( x +1)( x+2)} = \frac{A}{(x+1)}+\frac{B}{(x+2)}

\implies x = A(x+2)+B(x+1)

Now, equating the coefficients of x and constant term, we obtain

A+B =1

2A+B =0

On solving, we get

A=-1\ and\ B =2

\therefore \frac{x}{(x+1)(x+2)} = \frac{-1}{(x+1)}+\frac{2}{(x+2)}

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

=-\log|x+1| +2\log|x+2| +C

=\log(x+2)^2-\log|x+1|+C

=\log\frac{(x+2)^2}{(x+1)}+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 Central Sector Scheme of Scholarship 2025 applications open on scholarships.gov.in
anam-khan

CBSE Board 2025: Class 10th, 12th supplementary date sheet out; exams from July 15
anam-khan

CBSE issues final reminder to schools for supplementary exam LOC submission; submit by today without late fee

Latest Question