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Homework Help: Trigonometric substitution of (x^2+8x)

  1. May 24, 2014 #1
    1. The problem statement, all variables and given/known data
    Hello PF, I am taking calculus II right now, and a homework problem I came to ponder upon has been giving me big trouble today. Here is the what I have to take the integral of:

    ∫x/(x^(2)+8x)^(1/2) dx

    Every other trig substitution problems were straight forward, as all I had to do was identify what trig identity I could use. But this time, I have no idea where to start from.

    2. Relevant equations

    3. The attempt at a solution
    In wishful thinking I set substitution for x=(8^(1/2))tan(t), but as expected it didn't work out after.

    Help would be greatly appreciated!
  2. jcsd
  3. May 24, 2014 #2

    Simon Bridge

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    $$\int \frac{x}{\sqrt{x^2+8x}}\;dx$$... you need a substitution that makes the term inside the radical a complete square.

    That is the point behind trig substitutions.
    So try completing the square inside the radical first.
  4. May 24, 2014 #3
    OK, I didn't know how to complete a square until now. I tried, and I'm making progress now, thank you!
  5. May 24, 2014 #4

    Simon Bridge

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    You looked it up - well done :)
    Let me know how you get on.
  6. May 25, 2014 #5


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    Sorry, what I had here was not correct. I think the best thing is to remove it.
    Last edited: May 25, 2014
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