How do you integrate int (2x +1) / ((x - 2)(x^2 + 1)) using partial fractions?

1 Answer
Apr 1, 2016

int(2x+1)/((x-2)(x^2+1))dx=ln|x-2|-1/2ln(x^2+1)+c

Explanation:

int(2x+1)/((x-2)(x^2+1))dx=intA/(x-2)dx+int(Bx+C)/(x^2+1)dx
0x^2+2x+1=A(x^2+1)+(Bx+C)(x-2)
Equating coefficients:
A+B=0
C-2B=2
A-2C=1
Solving simultaneously yields A=1, B=-1 and C=0
=int1/(x-2)dx-intx/(x^2+1)dx
=ln|x-2|-1/2ln(x^2+1)+c