$\int \dfrac{x}{x^4+2x^2+2} dx$ Let u = √x ... ↔ ... u² = x. 2u du = dx $\int \dfrac{u^2}{u^2+2u+2} (2u\; du)\\ 2\int \dfrac{u^3}{u^2+2u+2} du$ Does that seem more doable?