Question

1. $\int\sec^{2}(x + 2)dx$

Explanation:

Step1: Use substitution

Let \(u = x + 2\), then \(du=dx\).

Step2: Integrate \(\sec^{2}u\)

We know that \(\int\sec^{2}u\ du=\tan u + C\) (where \(C\) is the constant of integration).
Substituting back \(u = x + 2\), we get \(\tan(x + 2)+C\).

Answer:

\(\tan(x + 2)+C\)