Set up partial fractions for 2x+3x(x2+1)\dfrac{2x+3}{x(x^2+1)}x(x2+1)2x+3.
Ax+Bx+Cx2+1\dfrac{A}{x} + \dfrac{Bx+C}{x^2+1}xA+x2+1Bx+C
Ax+Bx2+1\dfrac{A}{x} + \dfrac{B}{x^2+1}xA+x2+1B
Ax+Bx+Cx2+1\dfrac{Ax+B}{x} + \dfrac{C}{x^2+1}xAx+B+x2+1C
Ax+Bx+i+Cx−i\dfrac{A}{x} + \dfrac{B}{x+i} + \dfrac{C}{x-i}xA+x+iB+x−iC