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Integrating with radicals

  1. Feb 25, 2013 #1
    1. The problem statement, all variables and given/known data
    for the following integrals, am I allowed to break them up like so:

    1. ∫(1)/(sqrt(16-9x²)³) dx

    = ∫(1)/(√16)³ · ∫(1)/(√-9x²)³ dx

    2. ∫(x²)/(sqrt(x²-9)) dx

    = ∫(x²)/(√x²) · ∫(x²)/(√-9) dx

    3. ∫(1)/(x²(sqrt(a²+x²))) dx

    = ∫(1)/(x²) · ∫(1)/(√a²) · ∫(1)/(√x²) dx

    ? ? ?


    2. Relevant equations
    none


    3. The attempt at a solution
    I need to know if I'm allowed to break them up like this before I start attempting a solution
     
  2. jcsd
  3. Feb 25, 2013 #2

    eumyang

    User Avatar
    Homework Helper

    Is this what you are writing for #1?
    [itex]\int \frac{1}{\left( \sqrt{16-9x^2}\right)^3} dx[/itex]
    [itex]=\int \frac{1}{\left( \sqrt{16}\right)^3} dx \cdot \int \frac{1}{\left( \sqrt{-9x^2}\right)^3} dx[/itex]
    Yikes. No, you cannot do that!

    [itex]\sqrt{a - b} \ne \sqrt{a} \cdot \sqrt{-b}[/itex]
    Better review the properties of radicals.
     
  4. Feb 25, 2013 #3
    Ok, guess i'll try something else. Thanks
     
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