Keep in mind that

. (*)

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

(Verify)

Complete the square to get

(Verify)

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!