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:

∫ x^{n} dx = x^{n+1}⁄_{(n+1)}+ c

∫ k .dx = kx + c

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Trigonometry rules:

Example 1: ∫ x^{4} .dx

4x^{2} + c (b) 4x^{3} + c (c) ^{x3}⁄_{3 + c} (d) ^{x5}⁄_{5 + c}

Answer: d

Explanation: Here n = 4

∫ x^{4} dx =^{ x(4+1)}⁄_{(4+1)} + c

= ^{x5}⁄_{5} + c

Example 2: ∫(8e^{x}- ^{2}⁄_{x2} + 3x^{2} -2x). dx

Answer:

8 ∫e^{x} . dx - 2 ∫x^{-2} . dx + 3 ∫x^{2} .dx - 2 ∫x .dx

= 8e^{x} – 2.^{x-1}⁄_{-1} + 3. ^{x3}⁄_{3} - 2. ^{x2}⁄_{2 + c}

= 8e^{x} + ^{2}⁄_{x} + x^{3} - x^{2} + c