Why is the coefficient -2 instead of -2/3 in the improper integral solution?

[rmiller70015]

Homework Statement

$\int$ (x-2)^-3/2dx

Homework Equations

$\int$f(x)dx from 0 to ∞ = lim (t$\rightarrow$∞) $\int$f(x)dx from 0 to t

The Attempt at a Solution

I have the solution from the solution manual, but I'm just not sure on one of the steps, after you substitute u=(x-2) and du=dx, then integrate u^-3/2, but they say that the result to this step is lim(t$\rightarrow$∞) -2(x-2)^-1/2, that is when they integrate u^-3/2 they are getting a -2 coefficient, shouldn't it be a -2/3

 

[scurty]

Try taking the derivative of the answer to see why it is a -2.

$\int x^n dx = \frac{1}{n+1} x^{n+1}, n \neq -1$

 

[rmiller70015]

I'm ummm, I'm face palming right now, thanks.

 

[scurty]

It's okay. Everybody has done something similar at one point or another!