Hi, I am having difficulty getting to the end with this one...see attached
I take it you mean the original problem is , because the 2m term appears out of nowhere in the second step.
For the moment, let's focus on the exponent:
Rearranging, we get
Complete the square to get
With this, we can now evaluate this integral instead:
Now apply the substitution .
Thus, the integral becomes
Now apply (*) to get
which appears to be different from the answer you have supplied....so maybe I made a mistake somewhere??
But this is the idea of how to approach this problem. Hope this helps!
Then the rest of the problem becomes algebra once you apply the formula for the Gaussian.
Does this clarify things?