For an integer

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

For an integer

n\ge 1

, let

I_n = \displaystyle \int x^{n}e^{x}\,dx

. Derive an explicit relation that expresses

I_n

in terms of

I_{n-1}

and

x^{n}e^{x}