Question

Choose the correct alternative from the following.

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx"` = 

Options

• `(-1)/"x + 1"` + c

• `((-1)/"x + 1")^5` + c

• log(x + 1) + c

• log |x + 1|⁵ + c 

Answer 1

`(-1)/"x + 1"` + c

Explanation:

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx" = int ("x + 1")^3/("x + 1")^5` dx

`= int 1/("x + 1")^` dx

`= (-1)/"x + 1"` + c