Power of e

Calculus Level 5

\(\displaystyle I(r,n)=\int _{ -\infty }^{ 0 }{ { x }^{ r }{ e }^{ nx } \text{ d}x } \) where \(r,n \in \mathbb{Z} \).

\[\displaystyle X= \sum_{n=1}^{\infty } \sum_{r=0}^{\infty } \frac{1}{I(r,n)}\]

Find \(\left\lfloor { 10 }^{ 4 }X \right\rfloor\)

This is part of my set Powers of the ordinary.
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