`int(dx)/(sqrt(16-x^(2)))`

Answer

To solve the integral \( \int \frac{dx}{\sqrt{16 - x^2}} \), we can follow these steps:

### Step 1: Rewrite the Integral
We recognize that \( 16 \) can be expressed as \( 4^2 \). Thus, we can rewrite the integral as:
\[ \int \frac{dx}{\sqrt{4^2 - x^2}} \]

### Step 2: Identify the Formula
This integral resembles the standard form:
\[ \int \frac{dx}{\sqrt{a^2 - x^2}} = \sin^{-1}\left(\frac{x}{a}\right) + C \]
where \( a = 4 \).

### Step 3: Apply the Formula
Using the formula, we can substitute \( a = 4 \) into our integral:
\[ \int \frac{dx}{\sqrt{4^2 - x^2}} = \sin^{-1}\left(\frac{x}{4}\right) + C \]

### Step 4: Write the Final Answer
Thus, the final answer for the integral is:
\[ \int \frac{dx}{\sqrt{16 - x^2}} = \sin^{-1}\left(\frac{x}{4}\right) + C \]