a,b,x,t = var('a,b,x,t')
assume(t > 0)
integral((a^2+b^2*x^2)^(-1/2),x,0,t)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/bob/.sage/sage_notebook/worksheets/admin/1/code/9.py", line 8, in <module>
    integral((a**Integer(2)+b**Integer(2)*x**Integer(2))**(-Integer(1)/Integer(2)),x,Integer(0),t)
  File "/home/bob/sage/local/lib/python2.5/site-packages/sympy/plotting/", line 1, in <module>
    
  File "/home/bob/sage/local/lib/python2.5/site-packages/sage/misc/functional.py", line 437, in integral
    return x.integral(*args, **kwds)
  File "/home/bob/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py", line 2479, in integral
    raise TypeError, error
TypeError: 
Is  a  
Computation failed due to a bug in Maxima -- NOTE: Maxima had to be restarted.

// I then add the a > 0 assumption:

a,b,x,t = var('a,b,x,t')
assume(t > 0)
assume(a > 0)
integral((a^2+b^2*x^2)^(-1/2),x,0,t)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/bob/.sage/sage_notebook/worksheets/admin/1/code/10.py", line 9, in <module>
    integral((a**Integer(2)+b**Integer(2)*x**Integer(2))**(-Integer(1)/Integer(2)),x,Integer(0),t)
  File "/home/bob/sage/local/lib/python2.5/site-packages/sympy/plotting/", line 1, in <module>
    
  File "/home/bob/sage/local/lib/python2.5/site-packages/sage/misc/functional.py", line 437, in integral
    return x.integral(*args, **kwds)
  File "/home/bob/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py", line 2479, in integral
    raise TypeError, error
TypeError: Computation failed since Maxima requested additional constraints (use assume):
Is  t  positive, negative, or zero?