Evaluate: `intx/(x^4-x^2+1)\ dx`

Explanation

`int frac{x d x}{x^{4}-x^{2}+1} `

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

`Rightarrow 2 xdx=d t `

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

`text { Now, } int frac{x d x}{x^{4}-x^{2}+1} `

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

`=frac{1}{2} int frac{d t}{t^{2}-t+(frac{1}{2})^{2}-(frac{1}{2})^{2}+1} `

`=frac{1}{2} int frac{d t}{(t-frac{1}{2})^{2}+frac{3}{4}} d t `

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