Answer to Question #208679 in Calculus for Didues

Question

L^-1( s+5 / s² -6s +13)

Answer 1

Consider L^-1(s+5)/(s² - 6s +13)

= L^-1(s-3 + 5)/(s² -6s+13)

=L^-1 [(s-3)/((s-3)²+4)] + 8/((s-3)²+4)

= e^3t cos 3t + 8 (1/2) e^3t sin 3t

= e^3t cos 3t + 4 e^3t sin 3t