Using Laplace to solve a differential equation

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Use Laplace to solve x''+3x'+5x=sin(8t)
Initial conditions x(0)= 2 and x'= -3

I have worked it down to (s2+3s+5)X(s)= 2s+3+ [8/(s2+64)] but stuck. Please help
 

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Got it.
 

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Use Laplace to solve x''+3x'+5x=sin(8t)
Initial conditions x(0)= 2 and x'= -3

I have worked it down to (s2+3s+5)X(s)= 2s+3+ [8/(s2+64)] but stuck. Please help
Try completing the square on (s2+3s+5)
 

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