Példa

$\int {{5x-6}\over{x^2-2x+10}} dx={5\over2}\int {2x-{12\over5}\over{x^2-2x+10}} dx= {5\over2}\int {2x-2\over{x^2-2x+10}} dx-\int {1\over{x^2-2x+10}} dx=$

${5\over2}\ln(x^2-2x+10)-{1\over3}\arctan ({x-1\over3})$