Define the Problem

Consider the real-valued indefinite integral,

The integrand is a polynomial, and the analytic solution is

where $$k$$ is the constant of integration. Since the limits of integration are unspecified, the integral function family is not well-suited to solving this problem.

Express the Polynomial with a Vector

Create a vector whose elements represent the coefficients for each descending power of x.

p = [4 0 -2 0 1 4];

Integrate the Polynomial Analytically

Integrate the polynomial analytically using the polyint function. Specify the constant of integration with the second input argument.

k = 2;
I = polyint(p,k)

I = 1×7

    0.6667         0   -0.5000         0    0.5000    4.0000    2.0000

The output is a vector of coefficients for descending powers of x. This result matches the analytic solution above, but has a constant of integration k = 2.