After a trig sub I end up here: . . . . . no
This is a standard form: .
So we have: .
if you don't want to use the standard form for the answer, you could have used the trig substitution (after some algebraic manipulation), and you would arrive at the answer
(by the way, when you change the variable, the limits usually changes with it, in this case, when you went from t to , the limits would not be 2 to 4 anymore)
Why do we have to apply trig. sub.? Before that, I suggest to set
Since you'll have an easy integral to evaluate, and the conclusion follows.