Evaluate: `intx/(3x^4-18 x^2+11)\ dx`

Explanation

`int frac{x d x}{3 x^{4}-18 x^{2}+11} `

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

`Rightarrow 2 xdx=d t `

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

`text { Now, } int frac{x d x}{3 x^{4}-18 x^{2}+11} `

`=frac{1}{2} int frac{d t}{3 t^{2}-18 t+11} `

`=frac{1}{3 times 2} int frac{d t}{t^{2}-6 t+frac{11}{3}} `

`=frac{1}{6} int frac{d t}{t^{2}-6 t+9-9+frac{11}{3}} `

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