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Integral I can't Understand

  1. Jul 31, 2015 #1
    1. The problem statement, all variables and given/known data
    I have posted what appears to be the solution of this integral. I don't understand how the first integral was split apart in the 3rd line.

    2. Relevant equations
    The solution is included

    3. The attempt at a solution
    I have tried to break the integral apart but cant see how to do it...
     

    Attached Files:

  2. jcsd
  3. Jul 31, 2015 #2
    Looks like it might be integration by parts.
     
  4. Jul 31, 2015 #3
    what would be the assignment of u and dv? Does the way that he solved this problem make sense to you?
     
  5. Jul 31, 2015 #4
    Did you understand the second line? The third line is Int(uv)dx= u*int(v)dx- int{u'*(int v dx)}dx

    Here int=integration. latex is not working here
     
  6. Jul 31, 2015 #5
    It's a common formula, you must have learnt it. If you don't you will find it in your textbook. It's a necessary formula to do integration
     
  7. Jul 31, 2015 #6
    Good day. As Dr Courtney said it is in fact by parts. Once the integral is split into two let:

    [tex]u=x[/tex]
    [tex]du=dx[/tex]

    [tex]v=-2(x^{4}+1)^{-1/2}[/tex]
    [tex]dv=(4x^{3})/(x^{4}+1)^{3/2}[/tex]

    On the first integral.

    Good grief it's nearly impossible to type out latex on an iPad!!
     
  8. Jul 31, 2015 #7
    Here try this - take x2 out from the denominator , and then multiply - divide by two .

    See what happens .
     
  9. Jul 31, 2015 #8
    Thank you for your help.

    DeldotB..Thank you... I understood that it was probably integration by parts but it wasn't immediately obvious how to make the u and dv assignment.

    Qwertywerty..thank you. I took out an x^2 from the denominator and multiplied by 2 on top and bottom and then was able to let u = x^2 +x^(-2) but I would not have been able to have the presence of mind to have taken out the x^2 because I couldn't have foreseen what was going to happen...but thank you.


    I cannot use Latex and would like to learn....is there a way to learn to use latex?
     
  10. Jul 31, 2015 #9
    What you need is practice .
     
  11. Jul 31, 2015 #10
    I have been trying to find problems of a nature that will allow me to do that...
     
  12. Jul 31, 2015 #11
    Why don't you ask your teacher / a mentor here ?
     
  13. Jul 31, 2015 #12
    I don't have a teacher or mentor here....I dont know anyone here.....
     
  14. Jul 31, 2015 #13
    I meant a teacher at your school . You can always post at the academic guidance area if you don't want to ask your teacher .
     
  15. Jul 31, 2015 #14
    Thank you but I don't go to school...I am out of school....I am just trying to learn on my own....
     
  16. Jul 31, 2015 #15
    My bad . I'm not sure how that works .
     
  17. Aug 1, 2015 #16
    Qwertywerty....what was it that led you to take out an from the bottom
     
  18. Aug 1, 2015 #17
    Qwertywerty....what was it that led you to take out an x2 from the bottom
     
  19. Aug 1, 2015 #18

    Ray Vickson

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    What resources are you attempting to use? I recommend highly that you buy a copy of "Schaum's Outline of Calculus" (Google 'shaums outline series'). It starts at the elementary level and takes you through all the types of things you are asking about here; it has more than 1000 solved problems where you are taken step-by-step through the solution, and it is accompanied by instructional on-line videos. It is not expensive, ranging from about $6 to $14 (used) on Amazon.

    My apologies if you are using this already and it is still not enough.
     
  20. Aug 1, 2015 #19
    Well , I could see that taking x2 from the denominator would give you the derivative of the denominator - Practice

    I'm sorry if I've said something obvious .
     
    Last edited: Aug 1, 2015
  21. Aug 2, 2015 #20

    LCKurtz

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