Evaluate : (i) `intcos^(-1)xdx` (ii) `inttan^(-1)xdx` (iii) `intsec^(-1)xdx`

Explanation

To evaluate the integrals \( \int \cos^{-1}(x) \, dx \), \( \int \tan^{-1}(x) \, dx \), and \( \int \sec^{-1}(x) \, dx \), we will proceed step by step for each integral.

### (i) Evaluate \( \int \cos^{-1}(x) \, dx \)

1. **Substitution**: Let \( t = \cos^{-1}(x) \). Then, \( x = \cos(t) \).
2. **Differentiate**: Differentiate both sides to find \( dx \):
\[
dx = -\sin(t) \, dt
...