Need to show that:
There is a hint given that $x^3-1=(x-1)(x^2+x+1)$ but I don't seem to get how I could use it. If I try to integrate the expression on the left I get:
Which has some resemblance to the expression I am trying to come up with.
I know the expansion for $\arctan(x)$ function, but it does not involve sines. So can I arrive at this expression explicitly of should make some useful observations allowing me to incorporate sines into solution?