Integration ( 1 – cot x)/(1 + cot x) dx explain in great detail
write cotx as cosx/sinx
u get 1-(cos/sinx)divided by 1+(cosx/sinx)
u get (sinx-cosx)/(sinx+cosx)
substitute sinx+cosx=u
differentiate both sides
u get (cosx-sinx).dx=du
-(-cosx+sin x)dx=du
-cosx+sinx dx= -du
sinx-cosx dx=-du
substitute back in the integral expression
u get integral of(-du/u)
= -log u
substitute value of u