Question

#______ $y = e^{x + 2}$

Explanation:

Step1: Recall antiderivative rule

The antiderivative of \(e^{ax + b}\) is \(\frac{1}{a}e^{ax + b}+C\) (where \(a
eq0\) and \(C\) is the constant of integration). Here \(a = 1\) and \(b=2\).

Step2: Find the antiderivative of \(y'\)

Since \(y'=e^{x + 2}\), then \(y=\int e^{x+2}dx\). Using the rule above, we have \(y = e^{x+2}+C\).

Answer:

\(y = e^{x + 2}+C\)