Evaluate: `int1/(x\ sqrt(x^4-1))\ dx`

Explanation

`int frac{d x}{x sqrt{x^{4}-1}} `

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

`text { Let } x^{2}=t `

`Rightarrow 2 x=frac{d t}{d x} `

`Rightarrow x d x=frac{d t}{2} `

`text { Now, }=int frac{x d x}{x^{2} sqrt{(x^{2})^{2}-1}} `

`=frac{1}{2} int frac{d t}{t sqrt{t^{2}-1}} `

`=frac{1}{2} sec ^{-1}(t)+C `

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