`intx((sec2x-1)/(sec2x+1))dx`

Options

A. increases
B. does not change
C. first decreases and then increases
D. decreases

Explanation

To solve the integral \( I = \int x \frac{\sec^2 x - 1}{\sec^2 x + 1} \, dx \), we will follow these steps:

### Step 1: Rewrite the integrand
We start by rewriting the integrand using the identity \( \sec^2 x = 1 + \tan^2 x \):
\[ I = \int x \frac{\sec^2 x - 1}{\sec^2 x + 1} \, dx = \int x \frac{\tan^2 x}{\sec^2 x + 1} \, dx \]
Since \( \sec^2 x + 1 = 2 \sec^2 x \), we can simplify:
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