Question

What is the antiderivative of `2x`?

Answer 1

There are many antiderivatives of `2x`. The (most) general antiderivative is `x^2 +C`

Explanation:

An antiderivative of `2x` is a function whose derivative is `2x`:

antiderivatives include:

`x^2`, `" "x^2+7`, `" "x^2+19`, `" "x^2-11`, `" "x^2+(17pi)/8 - sqrt 21`

`x^2 +sin^2x+cos^2x`

Any (every) function that can be expressed in the form `x^2 + "some constant"` is an antiderivative.

The general antiderivative is expressed by choosing one of the antiderivatives and adding an "arbitrary constant" usually named `C`

It is convenient (but not required) to choose the first antiderivative on the list above and say:

The (most) general antiderivative of `2x` is `x^2 + C`.

Strange but true
According to the definition of general antiderivative, we can also say "The (most) general antiderivative of `2x` is `x^2+sin^2x+cos^2x+19sqrtpi - sqrt37/4 +C`"

Important! -- check you textbook's definition (and your grader's sense of humor) before using this smart-alecky answer on an exam!