Question

integral (e^t)*sin(t)+(e^t)*cos(t)

Answer 1

well, since the format is a product rule outcome ... undo the product rule

Answer 2

one of the useful formula!
\(\Large \int e^x (f(x)+f'(x))dx = e^x f(x)+c\)

take f(t) = sin t here, and it only works with e^x, not with any other exponent,