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 18.18 Question 7 Maths Textbook Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.18 Question 7 Maths Textbook Solution.

Answers (1)

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

Hint:  Let 3 \log x=2

Given: \int \frac{1}{x \sqrt{4-9(\log x)^{2}}} d x

Explanation:

            \int \frac{1}{x \sqrt{4-9(\log x)^{2}}} d x   ........(1)

        Let

        3 \log x=t

        \frac{3}{x} d x=d t \Rightarrow \frac{d x}{x}=\frac{d t}{3}

Put in (1)

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

                                      =\frac{1}{3} \sin ^{-1}\left(\frac{t}{2}\right)+c \quad\left[\int \frac{1}{\sqrt{a^{2}-x^{2}}} d x=\sin ^{-1}\left(\frac{x}{a}\right)+c\right]

                                       =\frac{1}{3} \sin ^{-1}\left(\frac{3 \log x}{2}\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

CBSE Board Result 2025 LIVE: Class 10th, 12th results by next week; DigiLocker codes, latest updates
anam-khan

Fake notice on CBSE 10th, 12th results 2025 in two-halves viral, board alerts students
anam-khan

CBSE Board Result 2025 LIVE: Class 10th, 12th results on cbse.nic.in soon; pass marks, DigiLocker code

Latest Question