So I have been trying to solve this equation,
The given answer is,
I began by using substitution to change the integral.
Substituting t back in
where t is taken from 0 to infinity.
Now if I take this answer minus the exponential, I can rearrange it to get the given answer
Which would mean that the exponential that this is multiplied by (taken from t = 0 to t = ) would have to equal 1. I'm having trouble with the exponential, but I can't think of any way that it could be equal to 1.
Where did I go wrong? I feel like I've made a stupid mistake somewhere, but I can't seem to find it.