Exercise
$\int\frac{x^3}{\left(x^3-1\right)^2}dx$
Step-by-step Solution
Final answer to the exercise
$\frac{1}{9\left(x+1\right)}+\frac{4\sqrt{3}}{27}\left(\frac{\sqrt{\left(3\right)^{3}}}{-8\left(\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\right)}-\frac{1}{2}\arctan\left(\frac{-1+2x}{\sqrt{3}}\right)+\frac{-\sqrt{3}\left(x-\frac{1}{2}\right)}{4\left(\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\right)}\right)+\frac{1}{9}\ln\left|x+1\right|+\frac{5\sqrt{3}}{27}\arctan\left(\frac{2\left(x-\frac{1}{2}\right)}{\sqrt{3}}\right)-\frac{1}{9}\ln\left|\sqrt{\left(x-\frac{1}{2}\right)^2+\frac{3}{4}}\right|+C_2$