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    Hi, can someone please help with out with this question.
    Integral of 8x/(2x+1)^0.5
    I know you would use u=2x+1 then differentiate it but then i dont know what to do next
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    Write the question out on your paper clearly and carfully adding all details, you can then see what and where to substitute in your u and your du
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    Are you sure you want to use u=2x+1?I don't remember off hand if that would be best. Maybe u^2=2x+1 seems more appropriate. Otherwise I think it'd leave you with either a partial fraction integration or an integration by parts. In any case, here's how you'd substitute:

    \int \dfrac{8x}{\sqrt{2x+1}},\dx
    so du=2dx we already have our two pieces to sub in.

    

\displaystyle \int \dfrac{4(u-1)}{\sqrt{u}} \dfrac{1}{2}\,du Here's what I was talking about. So it's clearly not the best substitution
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    Sorry i didnt mention but the question specifically says use u=2x+1 as the substitution. :p:
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    Okie dokie. does what I've written make sense? so you're substituting x=(u-1)/2 everywhere you see an x (including the limits if it was definite). Not forgetting to change your dx to du from the substitution equation you gave me (u=2x+1).
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    (Original post by pie_monster)
    Are you sure you want to use u=2x+1?I don't remember off hand if that would be best. Maybe u^2=2x+1 seems more appropriate. Otherwise I think it'd leave you with either a partial fraction integration or an integration by parts. In any case, here's how you'd substitute:

    \int \dfrac{8x}{\sqrt{2x+1}} dx
    so du=2dx we already have our two pieces to sub in.

    

\displaystyle \int \dfrac{4(u-1)}{\sqrt{u}} \dfrac{1}{2}\,du Here's what I was talking about. So it's clearly not the best substitution
    What's wrong with that?

    = \frac{1}{2}\displaystyle\int 4u^{\frac{1}{2}} - 4u^{-\frac{1}{2}} du

    easy to integrate.
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    Nice thanks! I got those answers in the end but for some reason Wolfram has a different answer.
    This is what it gives
    http://www.wolframalpha.com/input/?i...x/(2x%2B1)^0.5
 
 
 
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Updated: February 10, 2010

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