Let's start by proving that
Let
Now,
Q (i)prove that d/dx(artanhx)=1/(1-x^2)
this is just artanhx=y, tanhy=x then diff.
can't do simplify end of (ii) Q by using partial ractions and integrating deduce from this(ans to (i)) the logarithmic form of artanhx,,,i know the log form of artanhx is 1/2ln(1+x/1-x)???????
i did 1/(1-x^2) = (int)-1/(-2x-2) -(int)1/(2x-2)
giving 1/2ln|-2x-2| -ln|2x-2| then i get to 1/2ln|(-2x-2)/(2x-2)| not sure where to go from here i think its easy but im being ignorant,,,the log form of artanhx is 1/2ln(1+x/1-x)???????pls help!!!!
oh no wait when i use either the partial expantion of (x+1)(-x+1) or the base of (-x-1)(x-1) i still cant expand to get this,,
with (x+1)(-x+1) i get 1/2ln(2x+2)+l(x-1)
and with (-x-1)(x-1) i get 1/2ln(-2x-2)-1/2ln(2x-2) u know where to go from here??