Comment #5 on issue 1304 by akshaysrinivasan: Integrate sqrt(x**2 + y**2)
fails
http://code.google.com/p/sympy/issues/detail?id=1304
I tried this:
diff --git a/sympy/integrals/risch.py b/sympy/integrals/risch.py
index 81e2b7a..124ac38 100644
--- a/sympy/integrals/risch.py
+++ b/sympy/integrals/risch.py
@@ -186,12 +186,12 @@ def heurisch(f, x, **kwargs):
elif g.is_Pow:
if g.exp.is_Rational and g.exp.q == 2:
M = g.base.match(a*x**2 + b)
if M is not None and
M[b].is_positive:(M[b].as_coeff_terms()[0] > 0) :
if M[a].is_positive:
terms.add(asinh(sqrt(M[a]/M[b])*x))
elif M[a].is_negative:
terms.add(asin(sqrt(-M[a]/M[b])*x))
--------------
I tried adding this to the test_risch , and stumbled upon what I believe is
another
issue.
In the python intepreter, doing
>>> integrate(sqrt(x**2+y**2),x)
y**2*asinh(x*(y**(-2))**(1/2))/2 + x*(x**2 + y**2)**(1/2)/2
>>> (y**2*asinh(x*(y**(-2))**(1/2))/2 + x*(x**2 + y**2)**(1/2)/2).args
(y**2*asinh(x)/2, x/2)
>>> heurisch(sqrt(x**2+y**2),x,hints=[]) == \
... y**2*asinh(x*(y**(-2))**(1/2))/2 + x*(x**2 + y**2)**(1/2)/2
False
This works fine on isympy though. Isn't this a bug?
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