Math Help - Help with Change of Variables

1. Help with Change of Variables

$S(1+2x)^4(2)dx$

I need help figuring out how to differentiate the u and du along with writing out this problem. I would have asked questions in school today but I did not get to this problem when I was there. Can you help me understand what to do with the integer 4. Please help.

2. Originally Posted by Crimson
$S(1+2x)^4(2)dx$

I need help figuring out how to differentiate the u and du along with writing out this problem. I would have asked questions in school today but I did not get to this problem when I was there. Can you help me understand what to do with the integer 4. Please help.
Dear Crimson,

Did you mean, $\displaystyle\int2(1+2x)^4~dx$ ???

3. yeah I didn't know how to make that symbol. Thanks.

4. I still need help with the problem if that is okay

5. $\int (1+2x)^4 2dx$

Let $u=1+2x \rightarrow du=2dx$

your integral will be : $\int u^4 du$

should be easy now

6. Make the substitution $\displaystyle u = 1 + 2x$ so that $\displaystyle \frac{du}{dx} = 2$ and the integral becomes

$\displaystyle \int{u^4\,\frac{du}{dx}\,dx} = \int{u^4\,du}$.

I'm sure you can go from here.