A) n
B) \[n-1\]
C) \[n!\]
D) \[\left( n-1 \right)!\]
Correct Answer: D
Solution :
[d] \[{{I}_{n}}=\frac{{{d}^{n-1}}}{d{{x}^{n-1}}}[{{x}^{n-1}}+n{{x}^{n-1}}\log x]\] \[{{I}_{n}}=(n-1)!+n{{I}_{n-1}}\Rightarrow {{I}_{n}}-n{{I}_{n-1}}=(n-1)!\]
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