What is an antiderivative?

An antiderivative, also known as an indefinite integral, is the reverse process of differentiation. It involves finding a function that, when differentiated, will yield a given function.

For example, if f(x) is a function and F(x) is its antiderivative, then the derivative of F(x) with respect to x will be equal to f(x). In other words, F'(x) = f(x).

Antiderivatives are used in various areas of mathematics and science, including calculus, physics, and engineering. They allow us to find the original function when given information about its rate of change, and they are essential for solving many types of equations and problems.

Finding antiderivatives can sometimes be challenging, as it involves understanding the rules of integration and applying them correctly to different types of functions. Common techniques for finding antiderivatives include u-substitution, integration by parts, trigonometric substitutions, and using tables of integrals.