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Math Help - Integration Substitution Problem

  1. #1
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    Integration Substitution Problem

    I'm having issues with the following substitution problem:

    F (x^2+4x+7)^3(x+2)dx

    Am I correct in assuming that u=x^2+4x+7 and du=2x+2? or does du=x+2?

    Where do I go from here?
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi,
    Quote Originally Posted by NumbersNumbersNumbers View Post
    F (x^2+4x+7)^3(x+2)dx

    Am I correct in assuming that u=x^2+4x+7 and du=2x+2? or does du=x+2?
    If u=x^2+4x+7 then \frac{\mathrm{d}u}{\mathrm{d}x}=2x+4 so <br />
\mathrm{d}u=(2x+4)\mathrm{d}x=2(x+2)\mathrm{d}x

    Where do I go from here?
    Where do you want to go ?
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  3. #3
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    Quote Originally Posted by flyingsquirrel View Post
    Where do you want to go ?
    The math problem is for some homework, our instructor told us to "integrate the following expression via substitution". I'm stuck.
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by NumbersNumbersNumbers View Post
    I'm stuck.
    I don't understand why you are stuck. You were thinking about substituting u=x^2+4x+7, can you do this substitution ?


    \begin{cases}u=x^2+4x+7\\<br />
(x+2)\,\mathrm{d}x=\frac12\,\mathrm{d}u<br />
\end{cases} \implies \int (x^2+4x+7)^3(x+2)\,\mathrm{d}x=\int \ldots \mathrm{d}u
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