Determine the laplace transform k(t)=5t²e^-4t + sin(3t)
The laplace transform of t^n,e^(at) is: n! / (s - a)^(n+1)
Hence, the laplace transform of t^2,e^(-4t) is: 2! / (s - (-4))^(2+1) = 2/(s+4)^3
The laplace transform of sin(at) is: a/(s^2 + a^2)
Hence, the laplace transform of sin(3t) is: 3/(s + 9)
Then, the Laplace Transform of k(t) is K(s) = 10/(s+4)^3 + 3/(s + 9)