Originally Posted by

**wik_chick88** use contour integration to find the inverse Laplace transform of

$\displaystyle \frac{1}{s^3 + a^3}$

i thought i should first split the fraction, so I got

$\displaystyle \frac{1}{s^3 + a^3} = \frac{1}{(s+a)(s^2 - as + a^2)}$

but i tried to use partial fractions to split this fraction and it didn't work!

the inverse Laplace transform formula is

$\displaystyle f(x) = \frac{1}{2 \pi i}\int^{\gamma + i\infty}_{\gamma - i\infty} \frac{1}{s^3 + a^3}e^{sx} ds$

i'm not sure where to go from here!