How do you evaluate this integral: ∫ x^2/[(x^4)-1]

x^4 - 1 factorises into (x² + 1)(x² -1)

which further factorises into

(x² + 1)(x + 1)(x - 1)

Thus the integral becomes

x² /[(x² + 1)(x + 1)(x -1)

which can be resolved into partial fractions as

x² /[(x² + 1)(x + 1)(x -1) = (Ax + B) / ((x² + 1) + C / (x + 1) + D / (x - 1)

etc

1/4 (2 ArcTan[x] + Log[1 - x] - Log[1 + x])