What is the Antiderivative of (1-2x)/(x+1)?

1 Answer
Jun 18, 2018

int (1-2x)/(x+1)dx = -2 x+3 ln abs (x+1) +C

Explanation:

Solve the indefinite integral:

int (1-2x)/(x+1)dx

First reduce the degree of the numerator:

(1-2x)/(x+1) = - (2x-1)/(x+1) = -(2(x+1) -3)/(x+1) = -2+3/(x+1)

so, using the linearity of the integral:

int (1-2x)/(x+1)dx = -2 int dx +3 int dx/(x+1)

int (1-2x)/(x+1)dx = -2 x+3 ln abs (x+1) +C