Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.1 Definition of the Laplace Transform - Problems - Page 675: 3

$\dfrac{1}{(s-1)^2}$

The Laplace Transform can be written as: $L[F(t)]=\int_{0}^{\infty} e^{-st} f(t) dt $ We are given that $f(t)=te^t$ Now, $L[F(t)]=\int_{0}^{\infty} e^{-st} f(t) dt \\=\int_{0}^{\infty} e^{-st} [te^t] \ dt\\=\dfrac{1}{(s-1)^2} $