Comment #2 on issue 1060 by asmeu...@gmail.com:
integrate(sqrt(25-x)*sqrt(1+1/(4*(25-x))),x) can't do it
http://code.google.com/p/sympy/issues/detail?id=1060
If we were to allow integrate to ignore power combination rules, this would
work:
In [63]: b = integrate(cancel(sqrt((25-x)*(1+1/(4*(25-x))))), x)
In [64]: print b
2*x*sqrt(-x - x/(-4*x + 100) + 25 + 25/(-4*x + 100))/3 + 2*x*sqrt(-x -
x/(-4*x + 100) + 25 + 25/(-4*x + 100))/(3*(-4*x + 100)) - 50*sqrt(-x -
x/(-4*x + 100) + 25 + 25/(-4*x + 100))/3 - 50*sqrt(-x - x/(-4*x + 100) + 25
+ 25/(-4*x + 100))/(3*(-4*x + 100))
In [65]: cancel(cancel(b.diff(x) - powsimp(a, force=True)))
Out[65]: 0
Other interesting notes:
- The cancel call from within integrate() is necessary, or else it just
returns an unevaluated Integral (though it doesn't take very long).
The two cancel calls to reduce the result to 0 are necessary.
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