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Homework Help: Challenging Indefinite Integral e^arccos x

  1. Apr 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Integrate:
    ((e^arccos(x))(dx))/(sqrt(1-x^2))

    Image of the question is attached.

    2. Relevant equations



    3. The attempt at a solution

    I think i took the right first step for substitution:

    u=arccos(x);
    cos(u)=x;
    (du)(-sin(u))=dx

    Substituting u into the equation:
    ((e^u)(-sin(u))(du))/(sqrt(1-(cos(u))^2))

    This is where I'm stuck.
    I tried all of the following second substitutions, but they either took me in circles or didn't replace all the u variables, or took me back to square one:

    v=cos(u)
    v=e^u
    v=1-(cos(u))^2

    I am doing this for a Calculus project using the Maple 11 program. It seems to be able to integrate the problem just fine, but I can't figure it out.
    A .bmp image is attached if you are unsure of what I have typed for the question.
     

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  2. jcsd
  3. Apr 15, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    d/dx(arcosx) is not what you have. Recheck that.


    EDIT: nvm that.

    ↓↓↓↓↓↓↓↓↓↓↓
     
    Last edited: Apr 15, 2010
  4. Apr 15, 2010 #3
    cos^2(u) + sin^2(u) = .....
     
  5. Apr 15, 2010 #4
    Wow. I would say I can't believe how simple the question truly was, but trigonometric identities always get me. Thanks for pointing that out to me. I appreciate the help.
     
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