Evaluate: `intx/((1-x^4)^(3setminus2))\ dx` .

Explanation

`I=int frac{x}{(1-x^{4})^{3 / 2}} dx `

`int frac{}{2(1-mu^{2})^{3 / 2}} ~d mu quad mu=x^{2} `

`Rightarrow frac{1}{2} int frac{1}{cos ^{2} v} dv quad v=sin ^{-1} mu `

`frac{1}{2} tan (sin ^{-1}(x^{2})) `

`frac{1}{2} frac{{x}^{2}}{sqrt{1-{x}^{4}}} `

`I=frac{{x}^{2}}{2 sqrt{1-{x}^{4}}}+C`