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Homework Help: Integrate the holy arcsine x

  1. Jun 9, 2007 #1
    integrate the holy arcsine x :(

    1. The problem statement, all variables and given/known data

    The Integral arcsine (x) appears to be really problematic. I have to calculate the integral of sqrt(1-x^2). part of it is the arcsine x.

    Now I will ask only about arcsine x, and If any serious problem will occur i'll bother you with the another one :)

    2. Relevant equations

    3. The attempt at a solution

    I used Integration by parts , which was also suggested by someone on this site and forums (another forums which I accidentally wrote my question there).

    S(arcsine x)= {v=x u=arcsine x}
    xarcsine-S(x/sqrt(1-x^2)= {u= x v=arcsinx}
    S(arcsine x)

    What have I done wrong till now? Tried to look for different substitutions but didn't find anything of a value. moreoever, I just recently started studying it so have mercy :P

    Thanks in advance,
  2. jcsd
  3. Jun 9, 2007 #2


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    ok, to find [tex] \int \frac{x}{\sqrt{1-x^2}} dx [/tex], try the substitution [tex]x^2=u[/tex]. Can you take it from here?
  4. Jun 9, 2007 #3
    and what v is gonna be?
  5. Jun 9, 2007 #4


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    Its a substitution not an integration by parts.

    [tex] \int f(g(x))\frac{du}{dx}dx=\int f(u)du [/tex]

    Actually sid is it not better that x = sin(u) ?
    Last edited: Jun 9, 2007
  6. Jun 9, 2007 #5


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    Yes, that'd work as well.
    Last edited: Jun 9, 2007
  7. Jun 9, 2007 #6
    OMG it worked :P

    lot of thanks :)

    (didn't substitute x=sin(u) though (I'm not crazy))
  8. Jun 9, 2007 #7
    two new question, and yes I did try to solve it on my own too many times

    well that was part of S(sqrt(1-x^2)) which after six hours of trying I didn't manage to solve it.

    help? its driving me crazy.
    Question 2: solved myself, my brain is probably overheated if I asked weird stuff like it.
    and if somebody can guide me how to write here with formal syntax , I'll appreciate it.
    Last edited: Jun 9, 2007
  9. Jun 10, 2007 #8


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    Take a look at the https://www.physicsforums.com/showthread.php?t=8997" thread for this forum. Also, you can click on the latex images to see the code.

    To find, [tex]\int \sqrt{1-x^2} dx [/tex], try the substitution x=sin(u). Can you take it from here?
    Last edited by a moderator: Apr 22, 2017
  10. Jun 10, 2007 #9
    made it :P

    Mmm I already solved it yesterday without substituting :)

    if you want to know how i did ill be glad to tell.
    Last edited by a moderator: Apr 22, 2017
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