Question #236294

3) Find the inverse Laplace transform of ln(s+3/s²+9).

Explain the problem with step by step process?

Expert's answer

We are required to:

Inverse Laplace transform of ln(s+3/s²+9).

eat↔1s−a and sinωt↔ωs2+ω2.eat↔1s−a and sinωt↔ωs2+ω2.

With the theorem with a=−5a=−5 and ω=3–√ω=3

We obtain:

L−1(8s+5+7s2+3)=8L−1(1s+5)+7L−1(1s2+3)=8

L−1(1s+5)+73–√L−1(3–√s2+3)=8e−5t+73–√sin3–√t.

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