Inverse Laplace transform of s/(s²-s+17/4)

[END]

Homework Statement

Solve the following:

$$\mathscr{L}_s^{-1} \left\{ \frac{s}{s^2-s+\frac{17}{4}} \right\}$$

Homework Equations

Table of Laplace Transforms.

The Attempt at a Solution

The solution is
$$f(t) = (1/4 )e^{t/2} (\sin(2 t)+4 \cos(2 t))$$

I know I need to break up $F(s)$ into more common Laplace transforms, but I'm not quite sure how to begin.

 

[LCKurtz]

Homework Statement

Solve the following:

$$\mathscr{L}_s^{-1} \left\{ \frac{s}{s^2-s+\frac{17}{4}} \right\}$$

Homework Equations

Table of Laplace Transforms.

The Attempt at a Solution

The solution is
$$f(t) = (1/4 )e^{t/2} (\sin(2 t)+4 \cos(2 t))$$

I know I need to break up $F(s)$ into more common Laplace transforms, but I'm not quite sure how to begin.

Hint: Begin by completing the square in the denominator.