Evaluate: (i) `int1/(sqrt(a^2-b^2\ x^2))\ dx` (ii) `int1/(sqrt((2-x)^2+1))\ dx`

Explanation

(i)
`int frac{d x}{sqrt{a^{2}-b^{2} x^{2}}} `

`= int frac{d x}{sqrt{b^{2}(frac{a^{2}}{b^{2}}-x^{2})}} `

`= frac{1}{b} int frac{d x}{sqrt{(frac{a}{b})^{2}-x^{2}}} `

`= frac{1}{b} sin ^{-1}(frac{x b}{a})+C`


(ii)
`int frac{d x}{sqrt{(2-x)^{2}+1}} `

`text { let } 2-x=t `

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