1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Issues with u-Substitution

  1. Jul 2, 2012 #1
    1. The problem statement, all variables and given/known data
    I am struggling with u-substitution. I understand that it essentially the undoing of the chain rule, but I don not get how to actually go about the procedure.

    I have this example from my textbook:

    It says that u=x^2+1 and that du/2=xdx. Where did they get this from? How do I know what to use for u in any given equation. Once I have these to values (u and du) I know that it is just a matter of taking the integral andd then plugging x in for u. Any help is appreciated.
    Last edited by a moderator: Jul 2, 2012
  2. jcsd
  3. Jul 2, 2012 #2


    Staff: Mentor

    Do you know how to get the differential of u (i.e., du)?

  4. Jul 2, 2012 #3
    If I tske the derivative of u, then that should give me du/dx=something. I then multiply by dx to get du. Is that what you mean?
  5. Jul 2, 2012 #4
    That is right, you can treat it just like a fraction. Then isolate dx and substitute it into the original equation along with your U substitution. You'll lean what to substitute U for with experience. Basically, what ever you substitute U for, call it A for you'll end up with [itex]\frac{1}{\frac{d}{dx} A}[/itex]. If you do it right, this factor will cancel with some other x in the integral, leaving you with an integral only in terms of U du.
    Last edited: Jul 2, 2012
  6. Jul 2, 2012 #5
    Thank you for the replies. I'm sorry, but I don't understand anything about A. I have never heard of this before. Could you elaborate please?

    Also, are there any tricks to figuring out what u is?
  7. Jul 2, 2012 #6
    That is the "trick". I said let A represent whatever you substitute for U. Then when you follow the method you'll end up with 1 over A prime. Will post an example, just a sec.....
  8. Jul 2, 2012 #7


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    So, if [itex]\displaystyle u=x^2+1\,,[/itex] then [itex]\displaystyle \frac{du}{dx}=2x\,.[/itex]

    Therefore, [itex]\displaystyle du=2x\,dx\,,[/itex] correct ?

    Now, divide by 2.
  9. Jul 2, 2012 #8

    I forgot to write dx at the end of original function at top of page, I hope it's still clear.
    Last edited: Jul 2, 2012
  10. Jul 2, 2012 #9
    ^That right there just solved my problems. Thank you so much for your help everyone I really appreciate it.

    One more question though. How do I go about solving u-substitution problems for definite integrals? Is it the same but I plug in values of x and subtract at the end?
  11. Jul 2, 2012 #10
  12. Jul 4, 2012 #11
    One more thing, are there any tricks to realizing if a problem is u-substitution or integration by parts? Or is it merely just a matter of doing one to see if it works?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook