"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 f is called indefinite integral of f and represented:
∫ 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
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