Help with Change of Variables

**Crimson** · January 19th 2011, 04:51 PM

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

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.

**Sudharaka** · January 19th 2011, 04:54 PM

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

**Crimson** · January 19th 2011, 05:00 PM

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

**Crimson** · January 19th 2011, 05:18 PM

I still need help with the problem if that is okay

**Liverpool** · January 19th 2011, 05:55 PM

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

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

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

should be easy now

**Prove It** · January 19th 2011, 06:09 PM

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.

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