# Challenging Integral!

Calculus Level 3

Let $$\displaystyle I(n) = \int_1^e x^3 (\ln x)^n \, dx$$, where $$n$$ is a positive integer, find the value of $$\dfrac{4I(n) + nI(n-1)}{e^4}$$ for $$n\geq1$$.

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