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Thread: Integration Substitution Problem

  1. #1
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    Integration Substitution Problem

    I'm having issues with the following substitution problem:

    $\displaystyle F (x^2+4x+7)^3(x+2)dx$

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

    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
    $\displaystyle F (x^2+4x+7)^3(x+2)dx$

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

    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 $\displaystyle u=x^2+4x+7$, can you do this substitution ?


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