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Lecture in Indefinite Integrals

(Last Updated On: December 13, 2017)
Lecture on Indefinite Integral
“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:

F = int f(x),dx.

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

Lecture in Indefinite Integrals  (where n ≠ −1)

Lecture in Indefinite Integrals

Lecture in Indefinite Integrals

Lecture in Indefinite Integrals

Lecture in Indefinite Integrals

Lecture in Indefinite Integrals

Lecture in Indefinite Integrals

Lecture in Indefinite Integrals

Lecture in Indefinite Integrals

Lecture in Indefinite Integrals

Lecture in Indefinite Integrals

Integrating a Sum

Each term is integrated separately.

Lecture in Indefinite Integrals

Constant Factor in the Integrand

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

Lecture in Indefinite Integrals  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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