Calculus – Solve Antiderivative of a Function

HISTORY:  Derivation is very important in mathematics especially in calculus.
Appeared by the end of the 16th century, this concept was developed during 17th century, by a great German philosopher and scientist named Gottfried Wilhelm Leibniz (1646-1716) and also by a great English scientist and inventor named Sir Isaac Newtown(1642-1727).

PART 1:  The antiderivative is noted: ∫f(x) dx = F(x) + C

DEFINITION:
A function G(x) is an antiderivative of g(x) on an interval (a, b) if the derivative of F(x) = f(x) for all x in (a,b).

NOTATION:

NOTE:
Do not be confused by the terms ” antiderivative ” and ” ” indefinite integral ” they are the same.


EXAMPLE: Suppose, we have to find the antiderivative of function f

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