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

Explanation

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

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

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

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

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

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

`=frac{1}{3} times frac{1}{2 a^{3}} log |frac{x^{3}-a^{3}}{x^{3}+a^{3}}|+C `

`=frac{1}{6 a^{3}} log |`