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!

How do I do this integration by substitution?

  1. Jun 5, 2014 #1
    1. The problem statement, all variables and given/known data
    ∫1/(3+((2x)^.5))dx

    the answer should be ((2x)^.5) - 3ln(3+((2x)^.5)) + c

    I keep getting ((2x)^.5) - ln(3+((2x)^.5)) + c


    2. Relevant equations

    ∫1/(3+((2x)^.5))dx

    3. The attempt at a solution

    I did:

    u = 3 + ((2x)^.5)
    du = 1/((2x)^.5) dx

    du((2x)^.5) = dx

    so my integral is:

    ((2x)^.5) ∫ (1/u) du

    from there I integrated and got:

    ((2x)^.5) - ln(3+((2x)^.5)) + c

    Please explain this problem is driving me crazy.
     
  2. jcsd
  3. Jun 5, 2014 #2

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    You can't take the ((2x)^.5) outside the integral. x is not a constant!

    You substituted u = 3 + ((2x)^.5)
    so ((2x)^.5) = u - 3
     
  4. Jun 5, 2014 #3
    Ok, so I take the derivative of

    ((2x)^.5) = u - 3

    which gives me

    du = 1/((2x)^.5)

    I'm a bit confused, could you please elaborate on the steps?
     
  5. Jun 5, 2014 #4

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    You were doing OK the first time, as far as
    du((2x)^.5) = dx

    To do the substitution you need to get rid of ALL the x's.
    So need to find dx in terms of u and du, not x and du.
    That gives you
    du(u-3) = dx.
     
  6. Jun 5, 2014 #5
    Please excuse me if I'm sounding stupid

    So I do:

    (u-3)^2 = 2x

    I use chain rule on left side and get:

    2(u-3) = 2

    the 2's cancel and I get:

    du(u-3) = dx
     
  7. Jun 5, 2014 #6

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    You can do it like that if you want, but you already found
    du((2x)^.5) = dx
    and you know that
    ((2x)^.5) = u - 3
    so you can just substitute u-3 for ((2x)^.5)

    Either way, now have got
    du(u-3) = dx
    you can substitute that into the integral and finish the question.
     
  8. Jun 5, 2014 #7
    Thanks, I didn't see it that way till you showed me. I got the right answer now.

    Thanks a bunch!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How do I do this integration by substitution?
  1. How do I integrate (Replies: 4)

  2. How do I integrate (Replies: 8)

Loading...