Indefinite Integral

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Indefinite integral is the set of functions F(x) + C, where C is any real number and  F(x) is the integral of f(x) whereas Integral is the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x). In other words Indefinite integral is anti derivative of the functions. It is written as ∫ f(x)dx (without upper and lower limits).
If ∫ f(x)dx = F + c
Where F is the anti derivative of f and C is the arbitrary constant
Here f is called as integrand and x is the variable of integration.
Indefinite Integral is so called because it’s value can’t be determined until the end points are specified
Formulae:
∫ xn dx = xn+1(n+1)+ c
∫ k .dx = kx + c

Trigonometry rules:

Example 1: ∫ x4 .dx
4x2 + c          (b) 4x3 + c          (c) x33 + c          (d) x55 + c
Answer: d
Explanation: Here n = 4
∫ x4 dx = x(4+1)(4+1) + c
= x55 + c
Example 2: ∫(8ex- 2x2 + 3x2 -2x). dx
Answer:
8 ∫ex . dx - 2 ∫x-2 . dx + 3 ∫x2 .dx - 2 ∫x .dx
= 8ex – 2.x-1-1 + 3. x33 - 2. x22 + c
= 8ex + 2x + x3 - x2 + c

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