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Sir pls solve the following.
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Asked by rsudipto | 01 Jan, 2019, 10:20: AM
answered-by-expert Expert Answer
begin mathsize 12px style I subscript n space equals space integral open parentheses ln space x close parentheses to the power of n space d x space L e t space u space equals space open parentheses ln space x close parentheses to the power of n space comma space space d u space equals space n space open parentheses ln space x close parentheses to the power of n minus 1 end exponent 1 over x space d x d v space equals space d x comma space v space equals space x I subscript n space equals space x space open parentheses ln space x close parentheses to the power of n space minus space integral x space n space open parentheses ln space x close parentheses to the power of n minus 1 end exponent 1 over x space d x space space equals space x space open parentheses ln space x close parentheses to the power of n space minus space n integral space open parentheses ln space x close parentheses to the power of n minus 1 end exponent space d x space equals x space open parentheses ln space x close parentheses to the power of n space minus space n space I subscript n minus 1 end subscript H e n c e comma space space space I subscript n space plus space n space I subscript n minus 1 end subscript space equals space x open parentheses ln space x close parentheses to the power of n space plus C end style
Answered by Thiyagarajan K | 01 Jan, 2019, 11:28: AM

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