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

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Answer 1 · 2018-06-18T12:17:16

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

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#