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Math Help - Help with Change of Variables

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by Crimson View Post
    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 ???
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  3. #3
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    yeah I didn't know how to make that symbol. Thanks.
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  4. #4
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    I still need help with the problem if that is okay
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  5. #5
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    \int (1+2x)^4 2dx

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

    your integral will be : \int u^4 du

    should be easy now
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  6. #6
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    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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