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

Explanation

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

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

`= frac{1}{b^{2}} times frac{1}{2 frac{a}{b}} log |frac{frac{a}{b}+x}{frac{a}{b}-x}|+C[therefore int frac{d x}{a^{2}-x^{2}}=frac{1}{2 a} log |frac{a+x}{a-x}|+C] `

`= frac{1}{2 a b} log |frac{a+b x}{a-b x}|+c`



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

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