Evaluate the following :
(i) `int(x+(1)/(x))^(3//2)((x^(2)-1)/(x^(2)))dx " (ii) " int(sqrt(2+logx))/(x)dx`
(iii) `int((sin^(-1)x)^(3))/(sqrt(1-x^(2)))dx " (iv) " int(cotx)/(sqrt(sinx))dx`

Explanation

Let's solve each part of the question step by step.

### Part (i): Evaluate the integral
\[ \int \left(x + \frac{1}{x}\right)^{\frac{3}{2}} \cdot \frac{x^2 - 1}{x^2} \, dx \]

**Step 1:** Let \( t = x + \frac{1}{x} \).
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