Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.20 Question 6 Maths Textbook Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.20 Question 6 Maths Textbook Solution.

Answers (1)

Answer: x+\log \left|x^{2}-x+1\right|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c

Given: \int \frac{x^{2}+x+1}{x^{2}-x+1} d x

Hint: Using Partial Fraction

Explanation:

            Let

            I=\int \frac{x^{2}+x+1}{x^{2}-x+1} d x

   \frac{x^{2}+x+1}{x^{2}-x+1}=\frac{x^{2}-x+x+x+1}{x^{2}-x+1}=\frac{x^{2}-x+1}{x^{2}-x+1}+\frac{2 x}{x^{2}-x+1}

 =1+\frac{2 x-1}{x^{2}-x+1}+\frac{1}{x^{2}-x+1}

\int \frac{x^{2}+x+1}{x^{2}-x+1} d x=\int 1 d x+\int \frac{2 x-1}{x^{2}-x+1} d x+\int \frac{1}{x^{2}-x+\left(\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{2}+1} d x

                                =\int 1 d x+\int \frac{2 x-1}{x^{2}-x+1} d x+\int \frac{1}{\left(x-\frac{1}{2}\right)^{2}+\left(\frac{\sqrt{3}}{2}\right)^{2}} d x

                               =x+\log \left|x^{2}-x+1\right|+\frac{1}{\frac{\sqrt{3}}{2}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c

                                =x+\log \left|x^{2}-x+1\right|+\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c

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

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question