`int(sec^(2)x)/((2+tan x)(3+tan x))dx`

Explanation

To solve the integral \( \int \frac{\sec^2 x}{(2 + \tan x)(3 + \tan x)} \, dx \), we will follow these steps:

### Step 1: Substitution
Let \( t = \tan x \). Then, we have:
\[ \frac{d}{dx}(\tan x) = \sec^2 x \implies dx = \frac{dt}{\sec^2 x} \]
Substituting \( t \) into the integral gives:
\[ \int \frac{\sec^2 x}{(2 + t)(3 + t)} \cdot \frac{dt}{\sec^2 x} = \int \frac{dt}{(2 + t)(3 + t)} \]