Integration Formulas

There are many integration formulas but the formulas shown on the list below are the ones that are the most useful that you are likely to need when finding integrals and solving integration problems. Remember that all indefinite integrals differ by an arbitrary constant which is usually denoted by C.

Integration of Zero

Zero can be integrated but the integral of zero is just a constant, donated by C.

Integration of a Constant

The integration of a constant, in this case k, with respect to x, is k times x plus an arbitrary constant, C.

Integration of a continuous function f(x)

When there is a continuous function, f(x), the integral of the product of f(x) and a constant k is the product of the constant, k, and the integral of the function, donated by ∫f(x).

This is very useful in integration because whenever you are integrating a multiple of a function, you can pull out the constant and just integrate the function f(x).

Integration of the sum or difference of two functions, f(x) and g(x)

The integral of the sum or difference of two functions with respect to x is the sum or difference, respectively, of the integral of each function.

This is also very useful in integration because sometimes it is harder to integrate the sum or difference of functions than it is to integrate each function on its own then add them up or subtract them.