The app (android) Hiper Calc is rather powerful, with great CAS-capabilities. But it doesn't seem to have step functions, or Piecewise, or other ways to define conditional functions. I tried to mimic this by creating a function "Heaviside" as $\operatorname{HS}(x)= \frac{|x|+x}{2x}$
The graph of this results in:
But when I try to integrate this symbolically, it doesn't seem to succeed, due to the discontinuity at $x=0$.
I was hoping to get the exact solution for the indefinite integral, like $x\cdot\operatorname{Heaviside}(x)$.
Other CAS (SymPy, Maple,...) can do this, using step-functions or piecewise functions.
I've also been playing around a bit, defining functions like $\operatorname{test}(x): x\ge0$ (I know: strange to use an equation as a function definition...).
This strange function gives me "No solution exists" for test(-3), and "true" for test(3). Seems logical, but when I integrate that function, I get as a result: "$0.5x^2+c$", which I don't understand at all...
Someone can give me a hint? Is this beyond the limits of Hiper Calc? Or should I do this differently?