What is the integral of $int (x)/(x+1)^3 dx$ ?

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Answer 1 · 2016-02-04T17:56:28

$(-1)/(x+1) + 1/(2(x+1)^2)+C = (-2x-1)/(2(x+1)^2)+C$

$int (x)/(x+1)^3 dx = int (x+1-1)/(x+1)^3 dx$

$= int ((x+1)/(x+1)^3 - 1/(x+1)^3)dx$

$= int ((x+1)^-2 - (x+1)^-3)dx$

Let $u= x+1$ if you want to include those steps.

$= (-1)/(x+1) + 1/(2(x+1)^2)+C$

Do the algebra to get a single ration if you wish.

What is the integral of int (x)/(x+1)^3 dxint (x)/(x+1)^3 dx?