Question

Prove that the integral I(a) =
∞ 0
e−at−1 tet dt is convergent for any a > 0 and compute it. What about its uniform convergence?

Answer 1

\[I(a)=\int\limits\limits_{0}^{\infty}\frac{ e^(-at)-1 }{ te^t } dt , a>0\]

Answer 2

the power of e is -at