Question

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

Answer 1

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

Explanation:

`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`