Indefinite Integrals Formula, Definition, Properties, Examples

In calculus, two fundamental processes are differentiation and integration. Differentiation involves finding the derivative of a function, while integration is the inverse process of differentiation. In this discussion, we will focus on an essential concept in integration known as "integrals."

Indefinite Integrals Definition

Also Check - Derivatives Formula

Indefinite Properties

Property 5:

• ∫ 1 dx = x + C
• ∫ a dx = ax + C
• ∫ xn dx = ((xn+1)/(n+1)) + C ; n ≠ 1
• ∫ sin x dx = – cos x + C
• ∫ cos x dx = sin x + C
• ∫ sec2x dx = tan x + C
• ∫ cosec2x dx = -cot x + C
• ∫ sec x tan x dx = sec x + C
• ∫ cosec x cot x dx = -cosec x + C
• ∫ (1/x) dx = ln |x| + C
• ∫ ex dx = ex + C
• ∫ ax dx = (ax/ln a) + C ; a > 0,  a ≠ 1

Also Check - Differential Equation Formula

Indefinite Integrals Examples

Example 1:

Example 2:

Also Check - Vector Formula

Indefinite Integral vs Definite Integral