Get Answers to all your Questions

header-bg qa

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.9 question 17 maths textbook solution

Answers (1)


Answer:\frac{1}{3}(\log x)^{3}+c

Hint:Use substitution method to solve this integral.

Given:\int \frac{1}{x}(\log x)^{2} d x


        \begin{aligned} &\text { Let } I=\int \frac{1}{x}(\log x)^{2} d x \\ &\text { Put } \log x=t \Rightarrow \frac{1}{x} d x=d t \\ &\Rightarrow d x=x \; d t \text { then } \end{aligned}

        \begin{aligned} I &=\int \frac{1}{x} t^{2} \cdot x d t=\int t^{2} d t \\ &=\frac{t^{2+1}}{2+1}+c \quad\left[\because \int x^{n} d x=\frac{x^{n+1}}{n+1}+c\right] \end{aligned}

            \begin{aligned} &=\frac{t^{3}}{3}+c \\ &=\frac{1}{3}(\log x)^{3}+c \quad[\because t=\log x] \end{aligned}

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support