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Comment #10 on issue 1001 by matt...@gmail.com: Failure with definite integral of sqrt(R^2-x^2) and variations
http://code.google.com/p/sympy/issues/detail?id=1001

This indeed works now:

In [1]: var('R', positive=True)
Out[1]: R

In [2]: integrate(sqrt(R**2-x**2), x)
Out[2]:
 2     ⎛x⎞        ⎽⎽⎽⎽⎽⎽⎽⎽⎽
R ⋅asin⎜─⎟       ╱  2    2
       ⎝R⎠   x⋅╲╱  R  - x
────────── + ──────────────
    2              2

Moreover a test for the indefinite case was added when fixing 1304 (see test_issue_1304 in test_integrals.py). I submitted a pull request with a test for the definite case.

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