How can I integrate Sqrt[x^2-a] using trig substitutions?

[coverband]

Could someone show me how to integrate this. Bear in mind 'a' could be positive or negative thus i don't think we can use sqrt(a) in our answer...

 

[rock.freak667]

Well if a>0, then you can have sqrt(a) in your answer...

But for a<0 => -a>0 meaning that your integrand will become sqrt{x^2+b} where b=-a

 

[B-Rye]

Shouldn't matter if it's positive or negative, the integral is still the same, imaginary or not.

 

[mathwonk]

use trig substitutions, sec or tan depending on whether a is positive or negative.

 

[coverband]

use trig substitutions, sec or tan depending on whether a is positive or negative.

only problem is say if I use the substitution Let x = sqrt(a)Secy the integrated result has a tany in it