Question

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

Answer 1

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

Explanation:

`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.