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Homework Help: Integral of inverse trig or inverse hyperbolic

  1. Nov 17, 2011 #1
    1. The problem statement, all variables and given/known data

    ∫5/(4x√(9-16x2)dx

    2. Relevant equations

    I am pretty sure this is in the form of ∫du/(u√(a2-u2)

    3. The attempt at a solution

    setting u=4x a=3 and du=4dx so 1/4du=dx I get:

    -5/12 sech-1(4x/3) + C

    Is this right or am I using the wrong definition? Just trying to check my answers

    Thanks for any help
     
  2. jcsd
  3. Nov 18, 2011 #2

    HallsofIvy

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    Science Advisor

    Yes, that is correct.
     
  4. Nov 18, 2011 #3
    Thanks, I really appreciate it!

    One quick follow-up question to anyone who can help:

    Some of the integral definitions involving hyperbolic inverse functions call for if a>u or u>a. I know that dealing with a definite integral we just use the limits of integration to figure that out, but what if we are dealing with an indefinite integral? How do you know then?
     
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