arbitrary constant of integration | integration constant

Since the derivative of a constant is zero, any constant may be added to an indefinite integral (i.e., antiderivative) and will still correspond to the same integral. Another way of stating this is that the antiderivative is a nonunique inverse of the derivative. For this reason, indefinite integrals are often written in the form integral f(x) d x = F(x) + C, where C is an arbitrary constant known as the constant of integration. The Wolfram Language returns indefinite integrals without constants of integration. This means that, depending on the form used for the integrand, antiderivatives F_1 and F_2 can be obtained that differ by a constant.

constant | indefinite integral | integral | integration