Evaluate the following indefinite integrals :
`(i) intsqrt(a^(2)-x^(2))dx` `(ii) int(1)/(sqrt(49+x^(2)))dx`
`(iii) int(1)/(xsqrt(x^(6)-1))dx` `(iv) intsqrt((1+x)/(1-x))dx`
`(v) intsqrt((x^(2009))/(2x^(2008)-x^(2009)))dx` `(vi) int(1)/(sqrt((x-4)(x-5)))dx`

Explanation

Let's evaluate the given indefinite integrals step by step.

### (i) \( \int \sqrt{a^2 - x^2} \, dx \)

**Step 1:** Use the substitution \( x = a \sin \theta \). Then, \( dx = a \cos \theta \, d\theta \).

**Step 2:** Substitute into the integral:
\[
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