Inverse Laplace transformation | Inverse Laplace transformation formulas

Inverse Laplace transformation | Inverse Laplace transformation formulas


If laplace Transformation  of function f(t), L[F(t)] = f(s), then 

`L^{-1}[f(s)]=f(t)`

The various formulae of inverse Laplace Transformation are 

1. `L^{-1}[\frac{1}{s}]=1`

2. `L^{-1}[\frac{1}{s^{n}}]=\frac{t^{n-1}}{(n-1)!}`  if "n" is a positive integer

3. `L^{-1}[\frac{1}{s^{n}}]=\frac{t^{n-1}}{\Gamma (n)}`  if "n" is a fraction

4. `L^{-1}[\frac{1}{s-a}]=e^{at}`

5. `L^{-1}[\frac{1}{(s-a)^{n}}]=e^{at}\frac{t^{n-1}}{(n-1)!}`

6. `L^{-1}[\frac{a}{s^{2}+a^{2}}]=sinat`

7. `L^{-1}[\frac{a}{s^{2}-a^{2}}]=sinhat`

8. `L^{-1}[\frac{s}{s^{2}+a^{2}}]=cosat`

9. `L^{-1}[\frac{s}{s^{2}-a^{2}}]=coshat`

All the above results must be remembered for finding the inverse Laplace transformation of functions. 

Read Also :- Laplace Transformation formulae

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