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Question: Is there a direct way to have the int command return the anti-derivative plus an arbitrary constant of integration?

Question:Is there a direct way to have the int command return the anti-derivative plus an arbitrary constant of integration?

nmacsai 205 Maple 2021
integration constant int indefinite
January 09 2022
2

restart

NULL

Is there a direct way to have the int command return the anti-derivative plus an arbitrary constant of integration? I am imagining the process to look like:
int(f(x), x) = F(x)+c1

NULL

Consider the integral of f(x)=x.f := x

x

 (1)

Int(f, x); int(f, x)

(1/2)*x^2

 (2)

Notice that the output has no intregration constant or the constant has been assigned the value of zero and is not displayed in the output.

Maple 2021 Help states, "Indefinite integration  is performed if the second argument x is a name. Note that no constant of integration appears in the result. Definite integration is performed if the second argument is of the form x=a..b where a and b are the endpoints of the interval of integration."

I'd like Maple to output the anti-derivative plus an arbitrary constant in the same way dsolve outputs a general solution of an ode with arbitrary constants. My first work around was to just use dsolve.  

There is a sense in which performing an integration is equivalent to solving an ode:
diff(h(x), x) = g(x); int(diff(h(x), x), x) = int(g(x), x); h(x) = int(g(x), x)+c1; h(x) = G(x)+c2
    

Is there a way to force int to output arbitrary constants of integration or should I stick to just using dsolve if I want that effect?

Download constants_of_integration_int_output.mw
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