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!

Calculating indefinite integral

  1. Dec 12, 2011 #1
    1. The problem statement, all variables and given/known data

    hey could you help me to calculate the indefinite integral of y=√(x+1)/√(x+2)

    2. Relevant equations



    3. The attempt at a solution
    tried to set x+1=u and integrate it by substitution but didnt work
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Dec 12, 2011
  2. jcsd
  3. Dec 12, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Try to set [itex]u^2=x+1[/itex]
     
  4. Dec 12, 2011 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    It is not clear what your function y is. It could be [tex] y = \sqrt{x} + \frac{1}{x} + 2, [/tex] or [tex] y = \sqrt{\displaystyle x + \frac{1}{x}} + 2, [/tex] or
    [tex] y = \sqrt{\displaystyle x + \frac{1}{x} + 2}. [/tex] If you don't want to use LaTeX, you need to use brackets, so the first way I wrote above would be y = (√x) + (1/x) + 2, the second way would be y = √[x + (1/x)] + 2, and the thire way would be y = √[x + (1/x) + 2]. If I read your function using *standard* rules and priorities, it means the first way above.

    RGV
     
  5. Dec 12, 2011 #4
    So now you have ∫√u/(u+1)du. Try an additional substitution.
     
  6. Dec 12, 2011 #5
    I apologize for the missunderstanding the function is y=Sqrt[x+1]/Sqrt[x+2] i corrected it in the question to.
     
  7. Dec 12, 2011 #6
    well i tried it and this transformed the integral into ∫2*(u^3)/√(u^2+1)du. then i set u=tanθ and the integral is transformed into 2∫(tanθ^3)*secθdθ. and couldnt take it any further..
     
  8. Dec 12, 2011 #7

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    [itex] u = \sinh t [/itex] seems a better substitution.
     
  9. Dec 13, 2011 #8

    NascentOxygen

    User Avatar

    Staff: Mentor

    EDIT: double posting. see next post.
     
    Last edited: Dec 13, 2011
  10. Dec 13, 2011 #9

    NascentOxygen

    User Avatar

    Staff: Mentor

    I don't get that u^3.
     
  11. Dec 13, 2011 #10
    Indeed sinh does seem like a better option here
     
  12. Dec 13, 2011 #11

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Similar, but slightly different than what micromass suggested.

    Use the substitution: [itex]u=\sqrt{x+2}\,,[/itex] then [itex]\displaystyle du=\frac{dx}{2\sqrt{x+2}}\,.[/itex]

    This also gives [itex]\sqrt{x+1}=\sqrt{u^2-1}\,.[/itex]
     
  13. Dec 14, 2011 #12

    NascentOxygen

    User Avatar

    Staff: Mentor

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




Similar Discussions: Calculating indefinite integral
  1. Indefinite Integration (Replies: 11)

  2. Indefinite Integrals (Replies: 4)

  3. Indefinite Integral (Replies: 2)

Loading...