Question

Find the inverse Laplace transform for

1 / ((s^2+1)(s+1))

Answer 1

To find inverse Laplace transform for

Solution :

formula for inverse Laplace we'll be using in this problem

1)

2)

3)  

we perform the partial function of the function     , so as to bring it in the desired form .

So

Putting gives

Putting   gives

Putting

Therefore we get

Therefore

Simplifying further

So finally we take Laplace inverse of both side

Using Linear Property of Inverse Laplace

Now

Using Formula ( 1 )    

Using Formula (2 )   

Using Formula (3)  

Therefore We get

So answer is :

Inverse Laplace of    is :