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# Antiderivatives and indefinite integrals review

Review your knowledge of antiderivatives and indefinite integrals.

## What are antiderivatives and indefinite integrals?

Antiderivative is the reverse relation of derivative. For example, we know that the derivative of ${x}^{2}$ is $2x$. This means that an antiderivative of $2x$ is ${x}^{2}$.
${f}^{\prime }$ is the derivative of $f$ $\phantom{\rule{0.278em}{0ex}}⟺\phantom{\rule{0.278em}{0ex}}$ $f$ is an antiderivative of ${f}^{\prime }$
Each function has a family of antiderivatives. For example, the antiderivatives of $2x$ are the family of functions ${x}^{2}+c$ where $c$ can be any constant number.
The indefinite integral of a function can be viewed as exactly that, the family of antiderivatives of the function. It also has a special notation. For example, the indefinite integral of $2x$ is expressed as $\int 2x\phantom{\rule{0.167em}{0ex}}dx$.
In general, $\int {f}^{\prime }\left(x\right)\phantom{\rule{0.167em}{0ex}}dx=f\left(x\right)+c$.