Question

Find laplace transform of t+t^2 +t^3

Answer 1

Recall that

$L_s\left\{t^n\right\} = \dfrac{n!}{s^{n+1}}$

where $L_s\left\{y(t)\}$ is the Laplace transform of y(t) into the s-domain.

Then you have

$L_s\left\{t+t^2+t^3\right\} = \dfrac{1!}{s^{1+1}} + \dfrac{2!}{s^{2+1}} + \dfrac{3!}{s^{3+1}} = \boxed{\dfrac1{s^2} + \dfrac2{s^3} + \dfrac6{s^4}}$