Evaluate: `int(sqrt(tanx))dx`

Explanation

To evaluate the integral \( I = \int \sqrt{\tan x} \, dx \), we can use a substitution method. Here’s a step-by-step solution:

### Step 1: Substitution
Let \( t = \tan x \). Then, we know that:
\[ \frac{dt}{dx} = \sec^2 x \quad \Rightarrow \quad dx = \frac{dt}{\sec^2 x} \]
Also, we have:
...