“To integrate” is to find a function whose derivative is given. This process is called integration or anti-differentiation.

The term

*integral*may also refer to the notion of the antiderivative, a function*F*whose derivative is the given function*f*. In this case, it is called an*indefinite integral*and is written:

### Antiderivatives

**Indefinite Integrals**. If F is an antiderivative of a function f, i.e., F'(x) = f(x), then for any constant C, F(x) + C is another antiderivative of f(x). The family of all antiderivatives of

**is called indefinite integral of**

*f**and represented:*

**f**
∫ f(x) dx = F(x) + C

Example: =

### Basic Integration Formulas

(where **n ≠ −1**)

### Integrating a Sum

Each term is integrated **separately**.

### Constant Factor in the Integrand

A constant factor in the integrand can be written before the integral sign.

where c is a constant

Again,

**Indefinite Integral**is the family of functions that have a given function as a common derivative. The indefinite integral of*f*(*x*) is written: ∫*f*(*x*)*dx*.*credit: Renato E. Apa-ap, et al.©2013 www.PinoyBIX.com*