If I_ n = _ 1 ^ e ( _ e x )^ n d x is a positive integer), then I_ 2012 +(2012) I_ 2011 =

Mathematics · JEE Advanced · NTA Exams — Integral Calculus

If \(I_{n}=\int_{1}^{e}\left(\log _{e} x\right)^{n} d x\) is a positive integer), then
\(I_{2012}+(2012) I_{2011}=\)

1. \(I_{2011}+(2010) I_{2010}\)
2. \(I_{2013}+(2013) I_{2012}\)
3. \(I_{2011}+(2010) I_{2009}\)
4. \(I_{2012}-(2012) I_{2011}\)

Answer

(B) I_ 2013 +(2013) I_ 2012

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