Proving Laplace Transform for Complimentary Error Function - Step by Step Guide

[13senses]

Can anybody show me how to prove this Laplace transform which leads to a complimentary error function? Thanks!\int^\infty_0 \frac{\sqrt{a}}{\pi \sqrt{x} (x+a)} e^{-x} dx = e^a erfc(\sqrt{a})I don't know how to separate a factor of \sqrt{\pi} from the laplace transform.

 

[mathman]

Start with y=√x and manipulate the integrand.