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

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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


\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}


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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