Calculate the convolution of the two functions below using the Laplace

transform:

$1)$ h$($t$)=$u$($t$),$g$($t$)=$sin$(5$t$)$u$($t$)$

$2)$ h$($t$)=$e$^($t$)$u$($t$),$g$($t$)=$tu$($t$)$

$3)$ h$($t$)=$e$^($t$)$u$($t$),$g$($t$)=$sin$(5$t$)$u$($t$)$

answers:

$1)(1)/(5)(1-$cos$(5$t$))$

$2)-$t$+$e$^($t$)-1$

$3)(1)/(26)(5$e$^($t$)-$sin$(5$t$)-5$cos$(5$t$))$