some constant c
[some constant c|some constant c] An antiderivative of 3x^7 is a function of the form x^8 + C, where C is a constant.
Definition
some constant c An antiderivative of 3x^7 is a function of the form x^8 + C, where C is a constant. Every function of this form is an antiderivative of 3x^7.
Mechanism
some constant c The antiderivatives of sinx are functions of the form cosx + C, where C is a constant. Every antiderivative of cosx follows this structure, and finding them involves identifying such functions.
Effects
some constant c The Mean <a href='/en/entity/value-theorem'>Value Theorem</a>'s Corollary 2 states that if F and G are differentiable functions with F' (x) = G' (x), then F(x) - G(x) = C for some constant C. This leads to the theorem that every antiderivative of e* is of the form e* + C, where C is a constant.