Status: New
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 2239 by [email protected]: Change ratint to give an answer as
hyperbolic functions instead of logs.
http://code.google.com/p/sympy/issues/detail?id=2239
It is worth to have
integrate(1/(x**2-1))
-arctanh(x)
integrate(1/(x**4-1))
-(1/2)*arctanh(x)-(1/2)*arctan(x)
The idea is to modify standard algorithm (elementary decomposition).
So 1/(x**2-a**2) - thought to be elementary and irreducible and it's
integral is equal to -(1/a)arctanh(x/a)
May be the flag should be added to be able to switch between standard and
modified algorithms.
The modified one will help to solve ODE like
diff(f(x),x)+f(x)**2-1
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