What is the Integral of ##1/tan(x) dx##?

##lnabs(sinx) +C##

##1/tanx = cotx = cosx/sinx##

With ##u = sinx##, we get

##int1/tanx dx= intcotx dx##

## = int cosx/sinx dx##

Let ##u = sinx##, so ##du = cosx dx## to get

## = int 1/u du##

## = ln absu +C##

## = ln abs sinx +C##