Evaluate the following:
(i) `int(sec^(2)x)/(3+tanx)dx " (ii) " int(e^(x)-e^(-x))/(e^(x)+e^(-x))dx`
(iii) `int(1-tanx)/(1+tanx)dx " (iv) " int(1)/(1+e^(-x))dx`

Explanation

Let's evaluate the given integrals step by step.

### (i) Evaluate \( \int \frac{\sec^2 x}{3 + \tan x} \, dx \)

1. **Substitution**: Let \( t = 3 + \tan x \). Then, differentiate to find \( dt \):
\[ dt = \sec^2 x \, dx \quad \Rightarrow \quad dx = \frac{dt}{\sec^2 x} \]
...