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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 20

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 20

Answers (1)

Answer:x(\log_{e}x-1)+c

Hint: You must know about the integral rule of logarithm functions.

Given: \int \log_{e}xdx

Solution:

\int \log_{e}x.1dx

Using by parts

         \begin{aligned} &=\log _{e} x \int 1 d x-\int\left[\frac{d}{d x} \log _{\varepsilon} x \int 1 d x\right] d x \\ &=x \log _{e} x-\int \frac{1}{x} x d x \\ &=x \log _{\varepsilon} x-\int 1 d x \quad\quad\quad\quad\quad\quad\left [ \int x^{n} dx=\frac{x^{n+1}}{n+1}\right ]\\ &=x \log _{e} x-x+c \\ &=x\left(\log _{e} x-1\right)+c \end{aligned}                                      

 

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