Laplace inverse (3s+4)/(s^2+
4s+29)

Complete the square in the denominator to reveal a sum of squares:

Recall the Laplace transforms of sine and cosine,

as well as the frequency shift property,

where is the Laplace transform of .

Rewrite the given transform as

The inverse transforms then follows:

So we end up with (after some regrouping)

step-by-step explanation:

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