Integration Rules

Integration Rules

Integral of a Function

A function 𝜙(x) is called a primitive or an antiderivative of a function f(x), if 𝜙'(x) = f(x).

Integration Rules

1. Chain rule :
   ∫u.v dx = uv₁ – u'v₂ + u''v₃ – u'''v₄ + ……… + (–1)^n­–1 u^n–1v_n + (–1)ⁿ ∫uⁿ.v_n dx
   Where  stands for n^th differential coefficient of u and stands for n^th integral of v.
2. Sum Rule
   ∫(f + g) dx = ∫f dx + ∫g dx
3. Difference Rule
   ∫(f - g) dx = ∫f dx - ∫g dx
4. Multiplication by constant
   ∫cf(x) dx = c∫f(x) dx
5. Power Rule (n≠-1)
   ∫xⁿ dx = xⁿ⁺¹/(n+1) + C

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