Question

I'm trying to find the laplace of (t^2)e^t and am wondering if there's a way to do it without using convolution; convolution looks tempting since you have a product of two functions, but I'm trying to avoid it.

Answer 1

hey u can use this property
\[L[t^n.F(t)]=(1)^n.\frac{ d^n }{ ds^n }.F(s)\]
@Mendicant_Bias

Answer 2

so first we know\[L[e^t]=\frac{ 1 }{ s-1 }\\so \\L[t^2.e^t]=(-1)^2.\frac{ d^2 }{ ds^2 }(\frac{ 1 }{ s-1 })=\frac{ d^2 }{ ds^2}\frac{ 1 }{ s-1 }\]
this will do fine
@Mendicant_Bias