Can sympy integrate an expression with Heaviside in the denominator?

Question

I'd like to do something like:

integrate(1/(1 + Heaviside(x)),x)

It just returns Integral(1/(Heaviside(x) + 1), x) unevaluated.

The problem is that Heaviside(0), is not defined. In Mathematica, for example, there is the UnitStep function, which is like the Heaviside, except that UnitStep(0) is equal to 1. Can I mimic this in sympy?

I've tried Heaviside(x,1) and it doesn't work.

Answer 1

I don't think the problem is Heaviside(0). It's just that sympy doesn't have the code to handle this particular case in the integration routines. You can help it along by rewriting the Heaviside as a Piecewise:

In [36]: Integral(1/(Heaviside(x) + 1), x).rewrite(Piecewise).doit()
Out[36]: 
⎧x  for x < 0
⎪            
⎨x           
⎪─  otherwise
⎩2