Power of e

Calculus Level 5

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

X=n=1r=01I(r,n)\displaystyle X= \sum_{n=1}^{\infty } \sum_{r=0}^{\infty } \frac{1}{I(r,n)}

Find 104X\left\lfloor { 10 }^{ 4 }X \right\rfloor

This is part of my set Powers of the ordinary.
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