Indefinite Integrals

An indefinite integral has the form

When evaluated, an indefinite integral results in a function (or family of functions). An indefinite integral of a function f(x) is also known as the antiderivative of f. A function F is an antiderivative of f on an interval I, if F'(x) = f(x) for all x in I. This is a strong indication that that the processes of integration and differentiation are interconnected.

Table of Indefinite Integrals

The following tables list the formulas for antidifferentiation. These formulas allow us to determine the function that results from an indefinite integral. Since the formulas are for the most general indefinite integral, we add a constant C to each one. With these formulas and the Fundamental Theorem of Calculus, we can evaluate simple definite integrals.

The next table lists indefinite integrals involving trigonometric functions.

Note: After finding an indefinite integral, you can always check to see if your answer is correct. Since integration and differentiation are inverse processes, you can simply differentiate the function that results from integration, and see if it is equal to the integrand.

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