Question:

$\int \frac{x(1-x^2)}{1+x^4} dx = \int \left( \frac{x}{1+x^4} - \frac{x^3}{1+x^4} \right) dx = \frac{1}{2} \arctan x^2 - \frac{1}{4} \ln(x^4 + 1) + C$<br>[Put $x^2 = t$ in first part and $x^4 + 1 = t$ in second part]