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Homework Help: Integrate (((x)^2)/2 + 9)

  1. Sep 17, 2012 #1
    1. The problem statement, all variables and given/known data

    ∫√(((x)^2)/2 + 9) dx

    2. Relevant equations


    3. The attempt at a solution
    I'm having a horrible time trying to do it. Problem is, I don't know how to start. The only thing I can think of is using trigonometric substitution. But I don't know how to manipulate the function in order to make it fit. A hint would be greatly appreciated.

    *Edit* I made a mistake, it's
    ∫√(((x)^4)/2 + 9) dx I accidentally put it to the 2nd power instead to the 4th...
    Last edited: Sep 17, 2012
  2. jcsd
  3. Sep 17, 2012 #2


    Staff: Mentor

    Trig substitution is the way to go.

    Note that x2/2 = (x/√2)2.
    Draw a right triangle with vertical leg labeled x/√2 and horizonatal leg labeled 3. Work out a relationship between the angle θ and x.

    BTW, integration problems should not be posted in the Precalc section. I am moving this thread to the Calculus & Beyond section.
  4. Sep 17, 2012 #3
    I made a mistake on the equation to be integrated. It's to the power of 4, not 2. Does it still apply?
  5. Sep 17, 2012 #4


    Staff: Mentor

    x4/2 = (x2/√2)2

    Same advice as before, except label one leg (the opposite would be my choice) as x2/√2 instead of x/√2.
  6. Sep 17, 2012 #5


    User Avatar
    Science Advisor
    Homework Helper

    If it's sqrt(x^4/2+9) trig substitutions won't get you anywhere. You'd need special functions to do it.
  7. Sep 17, 2012 #6


    User Avatar
    Homework Helper

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