# Math Help - Inverse Laplace Transform

1. ## Inverse Laplace Transform

Find the inverse laplace transform :

$F(s) = \sqrt{ s + \sqrt{1+s^2}}$

2. Originally Posted by simplependulum
Find the inverse laplace transform :

$F(s) = \sqrt{ s + \sqrt{1+s^2}}$
Has this arisen from a problem you're working on or have you been asked point blank to find it?

3. Originally Posted by simplependulum
Find the inverse laplace transform :

$F(s) = \sqrt{ s + \sqrt{1+s^2}}$
If you mean Bromwich style, then look at this one first:

$\mathop\oint\limits_{H} e^{st}\sqrt{1+s^2}\,ds$ where $H$ is the contour below. It doesn't matter if this one doesn't have an inverse transform. Just first figure out how the integrand varies across the (finite) red-blue and yellow-green branch-cuts and also the remaining parts of the contour. Then try and extend that work to $F(s)$ above. However, this may not be the best contour to use.