With first method I don't get an answer. The second method I get. Why ?
How did you type those stars? They look different in the two examples. In the language we can use various stars: \[RawStar], \[FivePointedStar], \[Star], \[SixPointedStar], with possibly different meanings.
I tried with [RawStar] and [Star] and still no answer] with == from mathematica
Integrate alpha e^(-alpha x) from x=a to b
Integrate alpha*e^(-alpha*x) from x=a to b