Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Integrate the functions in Exercises 1 to 24. 1

Integrate the functions in Exercises 1 to 24.

    Q1.    \frac{1}{x - x^3}

Answers (1)

best_answer

Firstly we will simplify  the given equation :-

                     \frac{1}{x - x^3}\ =\ \frac{1}{(x)(1-x)(1+x)}

Let                         

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

By solving the equation and equating the coefficients of x2, x and the constant term, we get

                                   A\ =\ 1,\ B\ =\ \frac{1}{2},\ C\ =\ \frac{-1}{2}

Thus the integral can be written as :

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

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

or                                                                                    =\ \frac{1}{2} \log \frac{x^2}{1-x^2}\ +\ C

Posted by

Devendra Khairwa

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

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question