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: Integrate this one?

  1. Apr 14, 2010 #1
    how am i going to integrate this one?

    f(x) = sqrt( 1 + 1/x )

    sorry for not using the symbol.. because not so familiar with that .. ^.^
  2. jcsd
  3. Apr 14, 2010 #2
    try substituting tan u = x
  4. Apr 14, 2010 #3
    does tan u = x work with f(x) = sqrt( 1 + (e^x)/4 ) ?
  5. Apr 14, 2010 #4
    did you solve the earlier?

    it didn't work

    if tan u = (e^(x/2)) / 2 would work i guess
  6. Apr 14, 2010 #5
    waaaaaaa, how come, i get sqrt(4+ex)

    thats wierd
    Last edited: Apr 14, 2010
  7. Apr 14, 2010 #6
    how did you figure out ? By intuition ?
    sorry , i think i have some mistake on the earlier question i posted .

    i forgot to raise the power of x to 2
    the f(x) should be f(x) = sqrt( 1 + 1/(x^2) )

    sorry about that ..~
  8. Apr 14, 2010 #7


    User Avatar
    Homework Helper
    Gold Member

    Have you figured this one out yet?
  9. Apr 14, 2010 #8
    owho, if your question sqrt( 1 + 1/x ) then use tan u = sqrt(x)

    if sqrt( 1 + 1/(x^2) ) then use tan u = x

    hmm, there are many ways, but for me, i imagine of a triangle

    sqrt( 1 + 1/(x2) ) = (sqrt(x2+1))/ x

    hmm how should i draw the triangle,

    or wait until some other explanation people give,

    i try scanning my triangle for a while. ngahahaha
  10. Apr 14, 2010 #9
    View attachment scan0001.pdf

    there, hmm how do i choose those values on triangle by intuition i guess, try to make it same as your equation.

    im really good in english tough, i hope someone can explain it more detail
  11. Apr 14, 2010 #10
    haven't ..~ no idea before annoymage replied my post~

    annoymage : woww..~ never thought of that methods ...~
    Last edited: Apr 14, 2010
  12. Apr 14, 2010 #11


    User Avatar
    Homework Helper
    Gold Member

    In that case, you'll probably find it easiest if you make the substitution [itex]w=\frac{1}{x}[/itex] and integrate by parts once before making the trig substitution annoymage suggested. Give it a try and post your attempt.
  13. Apr 15, 2010 #12
    I don't think integration by parts will go anywhere.

    Integration tables.

    You can obtain the the first integration form by substitution.


  14. Apr 16, 2010 #13


    User Avatar
    Homework Helper
    Gold Member

    This is integration by parts. The tables of integrals are derived using the same methods of calculus taught to students.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook