Question

How do you evaluate the integral `int 1/(x-2)^(2/3)dx` from 1 to 4?

Answer 1

`int_1^4 (dx)/(x-2)^(2/3) = 3(root(3)2+1)`

Explanation:

`int_1^4 (dx)/(x-2)^(2/3) = [3(x-2)^(1/3)]_1^4 = 3(2^(1/3)-(-1)^(1/3))= 3(root(3)2+1)`