A) \[\frac{{{(ln\,x)}^{n}}}{x}+C\]
B) \[x{{(ln\,x)}^{n-1}}+C\]
C) \[x{{(ln\,x)}^{n}}+C\]
D) none of these
Correct Answer: C
Solution :
[c] \[{{I}_{n}}=x{{(\ln x)}^{n}}-\int{\frac{x(n){{(\ln x)}^{n-1}}}{x}}dx\] \[={{(\ln x)}^{n}}-n\,{{I}_{(n-1)}}\] or \[{{I}_{n}}+n{{I}_{n-1}}=x{{(\ln x)}^{n}}\]
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