# Integration w/ trig sub

1. Aug 18, 2013

### jhahler

1. The problem statement, all variables and given/known data

integral of sqrt(x^2-36)/x)

2. Relevant equations

sqrt(x^2-a^2) = asec(u)
Pythagorean identity

3. The attempt at a solution
I used trig sub on the x^2-36 and changed that to x=36sec(u) and dx= 36sec(u)tan(u). I simplified the square root in the numerator using sec^2(u)-1 = tan^2(u). This gave me (6tan(u)/36sec(u))(36sec(u)tan(u)) What trig identities do I need to proceed? Or did I use the wrong kind of trig sub? Any help is greatly appreciated in advance.

2. Aug 18, 2013

### tiny-tim

hi jhahler!
isn't that just tan2 ?

3. Aug 18, 2013

### rock.freak667

In your substitution, 'a' should be 6, not 36. Therefore your dx=6sec(u)tan(u).

After your change your numbers, and simplify, you will need to use the same trig identity you used in the beginning with tan^2(u).

4. Aug 19, 2013

### vanhees71

I don't understand why you do such a complicated substitution. Perhaps I don't understand your notation right. It's way easier to use
$$x=6 \sin u.$$

5. Aug 19, 2013

### tiny-tim

sec2 - 1 = tan2

sin2 - 1 = minus cos2