Mathematics

Problem

For

n\ge 0

let

I_n=\displaystyle\int_{0}^{1}x^{n}e^{x}\,dx

. A previously established relationship shows that

I_n=e-n\,I_{n-1}

for all integers

n\ge 1

. What is the value of

I_4

? a)

5e-8

9e-24

-7e+24

9e