Get Answers to all your Questions

header-bg qa

Provide Solution For R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Multiple Choice Questions Question 25 Maths Textbook Solution.

Answers (1)

Answer:

\log |1+\log x|+C

Given:

\int \frac{1}{x+x \log x} d x

Hint:

Using  \int \frac{1}{x} d x

Explanation:

Let I=\int \frac{1}{x+x \log x} d x

        \begin{aligned} &=\int \frac{1}{x(1+\log x)} d x \\ &=\int \frac{\frac{1}{x}}{1+\log x} d x \\ &=\int \frac{d t}{t} \end{aligned}                                    \text { [ Put } \left.1+\log x=t \Rightarrow \frac{1}{x} d x=d t\right]

       \begin{aligned} &=\log |t|+C \\ &=\log |1+\log x|+C \end{aligned}

Hence, \int \frac{1}{x+x \log x} d x=\log |1+\log x|+C

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads