I have a problem with Maple. I would like to compute following sum using differentiation:
This power series is convergent for x in (-1,1).
Now when integrating:
the result is: 1/2*arctan(t)-1/4*ln(t-1)+1/4*ln(t+1) .
The problem is that ln(t-1) is not defined for t in (-1,1). This is caused by integration of the equation:
But if I would integrate the equation in the following form:
then the result of int(%,t); is
which is defined for t in (-1,1).
So how can I deal with this? How can I force Maple to use the form 1/4*(1/(1-t)) instead of -1/4/(t-1) without having to rewrite it manually?