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Integration question involving square root

  1. May 16, 2017 #1
    • Member warned that an effort must be shown
    1. The problem statement, all variables and given/known data

    How to integrate

    ## \frac{dx}{dt}=\sqrt{\frac{k}{x}-1}##

    AND

    ## \frac{dx}{dt}=\sqrt{\frac{k}{x}+1}##

    k a constant here.

    I'm unsure what substitution to do.
    Many thanks in advance.

    2. Relevant equations


    3. The attempt at a solution

    I can't really get started as I'm unsure what substition is needed.
    I think a trig but don't know what?


    many thanks in advance.
     
  2. jcsd
  3. May 16, 2017 #2

    Ray Vickson

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    You need to show more effort. Just try lots of different things. Some of them will be a wast of time, but others should work. Trying it on your own first is the only way to learn.
     
  4. May 18, 2017 #3
    Try expressing your integrals in a form that can be found in a table of integrals. It took me two minutes to find the answer to your question. If you are supposed to derive your answer from first principles, at least you will have something to work towards.
     
  5. May 18, 2017 #4
    I've been warned already. cheers for the input though my good pal ;)
     
  6. May 20, 2017 #5

    haruspex

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    A good start would be to write as an integral, in as simple a form as you can, instead of leaving it as a differential equation.
    Next, look for a substitution that gets k out of the way. Then think about a trig substitution.
     
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