# Homework Help: Challenging Indefinite Integral e^arccos x

1. Apr 15, 2010

### bur7ama1989

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. Apr 15, 2010

### rock.freak667

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

EDIT: nvm that.

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Last edited: Apr 15, 2010
3. Apr 15, 2010

### Count Iblis

cos^2(u) + sin^2(u) = .....

4. Apr 15, 2010

### bur7ama1989

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.