$\displaystyle

\int_ \frac{\pi}{6}^ \frac{\pi}{2} cot(x)dx

$

I ended up switching the cot to the inverse of tangent. Then I put in sines/cosine for tangent. I then did a trig substitution.

u=sin(x)

du=cos(x)dx

However, I end up with this:

$\displaystyle ln1 - ln(1/2)$

ln1 is zero so I'm left with -ln(1/2).

The answer choices (this is mult.choice)

A. ln(1/2)

B. ln(2)

C. -ln(2-(sq.root of 3))

D. ln((sq.root of 3) -1)

E. None of the above

My answer key says A is the right answer, but I have NEGATIVE ln(1/2). I'm not sure where I went wrong. ??