1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integration by Parts

  1. Apr 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Use integration by parts to find:

    y=... if dy=arcsinh(x) dx

    2. Relevant equations


    3. The attempt at a solution

    I understand how to perform integration by parts. My problem here is, what are my 'v' and 'du'?
  2. jcsd
  3. Apr 25, 2008 #2


    User Avatar
    Homework Helper

    [tex]\int sinh^{-1}x dx[/tex]

    well [itex]dv\neq sinh^{-1}x dx[/itex] since to find v you'd need to integrate that and well obviously you can't do that. So [itex]u=sinh^{-1}[/itex] and [itex]dv=1dx[/itex].
  4. Apr 26, 2008 #3
    A good general tip is to take very hyperbolic function and every trig function and learn how to differentiate it or integrate it. That way you don't have to remember the tables of functions. If you like memorising tables though do it that way, but do both. :smile: Just a really good but obvious hint I picked up recently that I thought might be useful.

    It's generally a good idea to try and split arc functions into there [itex]\frac{1}{\text{trig function}}[/tex] equivalents first, I don't know if it's just me but that seems to work out better more often than not? Clearly here the substitution becomes much easier when you do this, but I find it's a good general rule..?
    Last edited: Apr 26, 2008
  5. Apr 27, 2008 #4


    User Avatar
    Science Advisor
    Homework Helper

    Hi hex.halo ! :smile:

    You have to do a substitution first, and then integrate by parts!

    Put x = sinha, dx = cosha da …

    and you get … ? :smile:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integration by Parts
  1. Integration by parts (Replies: 6)

  2. Integration by parts (Replies: 8)

  3. Integration by Parts (Replies: 8)