How to Calculate Indefinite Integral

Definite and indefinite integral notation

The indefinite integral is the foundational concept in integral calculus. It is the formalized statement of the antiderivative and consists of three basic elements. The first is the integral symbol, which appears without upper or lower bounds, as with a definite integral. The next element is the function from which you would like to calculate the antiderivative. Finally, the variable of integration is noted. All other values, including other variables, are held constants during the integration.

Instructions

1. 

   Divide the integral into more manageable pieces, if possible. For polynomials, you can integrate each term independently. For trigonometric functions, you can often use half-angle and double-angle identities to simplify a complex problem.

2. 

   Integrate the first portion of the problem. In this example, the variable "y" is treated as a constant since the variable of integration is "x." Add "1" to the exponent of the variable of integration and divide the entire term by the new exponent for this type of algebraic function.

3. 

   Repeat the integration process for each remaining term.

4. 

   Combine all the terms and add a constant of integration. This term is added; the derivative of a constant is zero, which means the antiderivative of "0," which can be assumed to be part of the original function, is a constant. You can only determine an exact value for this constant of integration if you have a set of initial conditions for the function you are integrating.

Tips & Warnings

• The integrals of some functions, like trigonometric functions, are given by definition, so you must either memorize them or look them up in mathematical reference tables.

References

• Hofstra University: Tutorials for Finite Math and Calculus