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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 10

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 10

Answers (1)

Answer: \frac{\left ( \log x \right )^{n+1}}{n+1}+c

Hint: You must know about the integration rule of logarithm function

Given: \int \frac{\left ( \log x \right )^{n}}{x}dx

Solution:

\int \frac{\left ( \log x \right )^{n}}{x}dx

Put  \log x = t and differentiate both sides, \frac{d}{dx}\log x= \frac{1}{x}

\frac{1}{x}dx=dt

I=\int t^{n}dt

= \frac{t^{n+1}}{n+1}+c                             [t = \log x]

=\frac{\left ( \log x \right )^{n+1}}{n+1}+c 

 

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