How to solve the integral of y=1/(x-2)^1/3?

We'll use substitution technique to solve the
integral.

We'll put x - 2 =
t.

We'll differentiate both
sides:

dx = dt

We'll re-write
the integral in t:

Int dx/(x-2)^1/3 = Int
dt/t^1/3

We'll use the negative power
rule:

1/t^1/3 = t^(-1/3)

Int
dt/t^1/3 = Int t^(-1/3)dt

Int t^(-1/3)dt = t^(-1/3 +
1)/(-1/3 + 1) + C

Int t^(-1/3)dt = t^(2/3)/(2/3) +
C

Int dx/(x-2)^1/3 = [3(x-2)^(2/3)]/2 +
C