Evaluate: `int(x^2)/(x^6-a^6)dx`

Explanation

`int frac{x^{2}}{x^{6}+a^{6}} d x `

`Rightarrow int frac{x^{2} d x}{(x^{3})^{2}+(a^{3})^{2}} `

`text { let } x^{3}=t `

`Rightarrow 3 x^{2} d x=d t `

`Rightarrow x^{2} d x=frac{d t}{3} `

Now, `int frac{x^{2}}{x^{6}+a^{6}} d x `

`=frac{1}{3} int frac{a^{2}}{t^{2}+(a^{3})^{2}} `

`=frac{1}{3 a^{3}} tan ^{-1}(frac{t}{a^{3}})+C `

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