Question

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

Answer 1

Recall that

`L_s\left\{t^n\right\} = (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\} = (1!)/(s^(1+1)) + (2!)/(s^(2+1)) + (3!)/(s^(3+1)) = \boxed{\frac1{s^2} + \frac2{s^3} + \frac6{s^4}}`