In this example, g(t) = cos at and from the Table of Laplace Transforms, we have:

`G(s)= Lap{cosat}` `=s/((s^2+a^2))`

Now, applying the first rule above, we have:

`Lap{int_0^tcosat\ dt}=1/sxxs/(s^2+a^2)`

`=1/(s^2+a^2)`