I'm thinking this is undefined (except where a=b). Playing with integrating a=2, b=1 from 0 to 10, 100, 1000, 10000 etc. Adding a zero increases the integral by more than 1.
The integral formula for arctan has a ln term that seems to grow as well.
The real evidence was to change to the inverse of the function.
∞
∫ Arctan(
ax)−Arctan(
bx) dx =
0
π/2
∫ (1/a)tan(x)−(1/b)tan(x) dx =
0
π/2
(1/a1/b)∫ tan(x) dx
0
The integral formula for tan(x) is
lncos(x) which is undefined at π/2

Posted by Jer
on 20140404 22:02:57 