>> If we let y=e^t, shouldnt
the numerator be 1 instead of e^t in order to deduce? Correct me if
im wrong. So is the question given wrong?
The question is okay. If you are integrating with respect to y,
you must have "dy" at the end of the integral and not "dt". The
purpose of the e^t in the numerator is to combine with the "dt" to
give you "dy".
Since y = e^t
⇒ dy/dt = e^t
⇒ dy = e^t dt