How to integrate without limits in SymPy?

Question

I am given `p(x) = 2ax^2 - b` and asked to integrate it twice, but I'm not given limits. However, when I just use `integrate`, I'm not given a constant of integration, which is crucial to the next step. Since I don't have limits, using `scipy.integrate.dblquad` didn't work. Instead, I am importing `integrate` from SymPy and doing two separate integrals. This is what I have: from sympy import integrate x = Symbol('x') a = 240 b = 160 f = 2*a*x**2 - b g = integrate(f) h = integrate(g) What I want to get is: g = 160*x**3 - 80*x**2 + C h = 40*x**4 - 80*x**2 + Cx + c where `C` and `c` are constants of integration. My code currently produces the equations without the constants.

Answer 1

Sympy integrate doesn't include the constant, if you want to solve with a constant, you should use the dsolve function. For example, if you have p(x) = 2ax^2 - b, you can define r'(x) = p(x) = 2ax^2 - b, where r'(x) indicates the first derivative of r with respect to x. You simply have to then define r''(x) = p(x) = 2ax^2 - b to do a double integration.