William,

I notice that you're running a version of Axiom from Nov 2004.
In the latest version I get:


Starts dribbling to bug361.input (2007/9/8, 20:55:12).
(1) -> )set mes auto off
(1) -> integrate(1/(-3+v^3)*v/(-4*v^3)^(1/2),v)

   (1)
       -
             6+---+ +-+
            4\|- 1 \|3
         *
            atan
                  6+---+ +-+
                 3\|- 1 \|3
              /
                           +--------------------------------------------+
                           |   6+---+6+---+ +---+     6+---+2    6+---+2
                    6+---+ |- 3\|- 1 \|243 \|- v  - v \|243   + 9\|- 1
                   2\|243  |--------------------------------------------
                           |                   6+---+2
                          \|                   \|243
                 + 
                    6+---+ +---+    6+---+
                   2\|243 \|- v  - 3\|- 1
     + 
       -
             6+---+ +-+
            4\|- 1 \|3
         *
            atan
                  6+---+ +-+
                 3\|- 1 \|3
              /
                           +------------------------------------------+
                           | 6+---+6+---+ +---+     6+---+2    6+---+2
                    6+---+ |3\|- 1 \|243 \|- v  - v \|243   + 9\|- 1
                   2\|243  |------------------------------------------
                           |                  6+---+2
                          \|                  \|243
                 + 
                    6+---+ +---+    6+---+
                   2\|243 \|- v  + 3\|- 1
     + 
       6+---+     6+---+6+---+ +---+     6+---+2    6+---+2
       \|- 1 log(3\|- 1 \|243 \|- v  - v \|243   + 9\|- 1  )
     + 
        6+---+    6+---+ +---+    6+---+     6+---+    6+---+ +---+    6+---+
       2\|- 1 log(\|243 \|- v  + 3\|- 1 ) - 2\|- 1 log(\|243 \|- v  - 3\|- 1 )
     + 
         6+---+       6+---+6+---+ +---+     6+---+2    6+---+2
       - \|- 1 log(- 3\|- 1 \|243 \|- v  - v \|243   + 9\|- 1  )
  /
       6+---+
     12\|243
                                          Type: Union(Expression Integer,...)
(2) -> )spool


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