What is the solution to this basic integral using substitution?

[efekwulsemmay]

Homework Statement

Intergrate:

$$\int\frac{3 dx}{\left(2-x\right)^{2}}$$
By substituion.

Homework Equations

n/a

The Attempt at a Solution

Ok so first I take the integer out to get:

$$3\cdot\int\frac{dx}{\left(2-x\right)^{2}}$$

Now I let u = 2 - x and du = dx to get:

$$3\cdot\int\frac{du}{u^{2}}$$

Now I take away the fraction:

$$3\cdot\int u^{-2} du$$

Now I am stuck at this point. Any help would be apppreciated.

 

[micromass]

This is a basic integral, with this I mean that such integral should be learned by heart.
You have that (if $$n\neq -1$$ )

$$\int{x^ndx}=\frac{1}{n+1}x^{n+1}+C$$

Just apply this formula with n=-2.

 

[silvermane]

well, pretend that u^-2 is your x.

Do you know how to integrate x^-2?
(u⁻² ⁺¹)/(-2+1) + c is what you get.
don't forget that you still have that whole integral multiplied by 3.

When you're all finished, just substitute your 2-x back in and you've done the integral!

 

[efekwulsemmay]

This is a basic integral, with this I mean that such integral should be learned by heart.
You have that (if $$n\neq -1$$ )

$$\int{x^ndx}=\frac{1}{n+1}x^{n+1}+C$$

Just apply this formula with n=-2.

I just found a sheet with a few calc problems at my tutoring job and its been months since I did any calc so I decided to brush up a bit and test how much i remembered. Obviously not much all things considered but you've refreshed my memory. Thanks :)