Problem $1$:

A dynamic system with input $u(t)$ and output $y(t)$ has the transfer function representation

$G_p(s)=\frac{n(s)}{d(s)}=\frac{5s+1}{s^4+4s^3+3s^2+2s+1}.$

Obtain an all$-$integrator block diagram representation by expressing the transfer function as

$G_p(s)=\frac{Y(s)}{U(s)}=\frac{x(s)}{U(s)}\frac{Y(s)}{x(s)}=\frac{1}{d(s)}\frac{n(s)}{1}.$