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Intriguing Integral Illation II (Posted on 2014-04-03) Difficulty: 3 of 5
Evaluate this integral in terms of a and b, where each of a and b is a positive real number.


∫ Arctan(ax)−Arctan(bx) dx
0

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Ummm... | Comment 1 of 2
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/a-1/b)∫ tan(x) dx
              0

The integral formula for tan(x) is
-ln|cos(x)| which is undefined at π/2
  Posted by Jer on 2014-04-04 22:02:57
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