How do you evaluate the integral $int 1/(x+1)^3dx$ from -2 to 2?

Question

1794 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-30T01:31:21

$int_(-2)^2 frac 1 ((x+1)^3) dx =-4/9$

$int_(-2)^2 frac 1 ((x+1)^3) dx = int_(-2)^2 frac 1 ((x+1)^3) d(x+1) =$

$= -1/2 frac 1 ((1+x)^2) |_(x=-2)^(x=2) =$

$= -1/2 frac 1 ((-2+1)^2) +1/2 frac 1 ((2+1)^2) = -1/2+1/2 * 1/9 =$

$=1/2(1/9 -1) = -1/2 * 8/9 =-4/9$

How do you evaluate the integral int 1/(x+1)^3dxint 1/(x+1)^3dx from -2 to 2?