Homework Help: Evaluate integral using substitution

1. Feb 25, 2010

Col Musstard

1. The problem statement, all variables and given/known data
evaluate using substitution
Integral [cos^-1 x]/sqrt[1-x^2] dx

2. Relevant equations

3. The attempt at a solution
I am just starting with integration and I am getting frustrated with this problem. If someone could show me how to setup and start this problem so I could attempt to continue by reading instructions from my textbook it would be greatly appreciated

2. Feb 25, 2010

vela

Staff Emeritus
Hint: What's the derivative of $cos^{-1} x$?

3. Feb 25, 2010

Col Musstard

that is -1/sqrt[1-x^2] isnt it

4. Feb 25, 2010

vela

Staff Emeritus
Yup. Note that it's the other part of the integrand, so that means you should use a substitution.

5. Feb 25, 2010

Col Musstard

so u=cos^-1x. therefore du=-1/sqrt[1-x^2] dx
is this correct so far?

I got -[[cos^-1x]^2]/2 +c hope its right, thanks for the help

Last edited: Feb 25, 2010
6. Feb 25, 2010

vela

Staff Emeritus
Yes, that's the correct answer. You can always differentiate what you got and see if you get back the integrand.