Challenging Indefinite Integral e^arccos x

[bur7ama1989]

Homework Statement

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

Image of the question is attached.

Homework Equations

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.

 

[rock.freak667]

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


EDIT: nvm that.

↓↓↓↓↓↓↓↓↓↓↓

 

[Count Iblis]

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

 

[bur7ama1989]

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

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.