How do we integrate ln| 1 - cot x | 0-pi/4?

Answer 1

1-cotx=1-(cosx/sinx)= 1 - ((1/2)(cot(x/2))) - ((1/2)(sec(x/2)))
how to simplify this inside "ln"?

can we substract them adding ln(loge) infront of them?

Answer 2

I think you're stuck. There's just no way to get things to just a product.

According to wolframalpha, the integral is not elementary.

http://www.wolframalpha.com/input/?i=integral+log(1-cotx)+dx