\int \frac{\sqrt{2}-x}{x^2-\sqrt{2}x+1} \, dx=-\frac{1}{2}\int \frac{2x-2\sqrt{2}}{x^2-\sqrt{2}x+1} \, dx=-\frac{1}{2}\int \frac{2x-\sqrt{2}}{x^2-\sqrt{2}x+1} \, dx+\frac{1}{2}\int \frac{\sqrt{2}}{x^2-\sqrt{2}x+1} \, dx