Evaluate integral using substitution

[Col Musstard]

Homework Statement

evaluate using substitution
Integral [cos^-1 x]/sqrt[1-x^2] dx

Homework Equations

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

 

[vela]

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

 

[Col Musstard]

that is -1/sqrt[1-x^2] isn't it

 

[vela]

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

 

[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

 

[vela]

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