Explanation The given function is L − 1 { 1 s 3 ( s − 1 ) } . The inverse Laplace transform of the integral is, L − 1 { F ( s ) s } = ∫ 0 t f ( τ ) d τ , where f ( t ) = L − 1 { F ( s ) } . (1) Write the given function in the form of equation (1) as, L − 1 { 1 s 3 ( s − 1 ) } = L − 1 { 1 s 2 ( s − 1 ) s } . Compare the above equation with equation (1) and obtain F ( s ) = 1 s 2 ( s − 1 ) . Re write the above function as, F ( s ) = s − ( s − 1 ) s 2 ( s − 1 ) = s s 2 ( s − 1 ) − s − 1 s 2 ( s − 1 ) = 1 s ( s − 1 ) − 1 s 2 = s − s + 1 s

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Chapter 4.4, Problem 37E

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The inverse Laplace transform of the given function.

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Chapter 4.4, Problem 36E

Chapter 4.4, Problem 38E

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The inverse Laplace transform of the given function.

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