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Integration Formulas

1. Common Integrals
2. Integrals of Rational Functions
3. Integrals of Exponential Function
4. Integrals of Logarithmic Functions
5. Integrals of Trig. Functions

Common Integrals Formula PDF

1. Basic Integration Formulas
2. Integral of special functions
3. Integral by Partial Fractions
4. Integration by Parts
5. Other Special Integrals
6. Area as a sum
7. Properties of definite integration

Basic Formula

• ∫x n   = x n+1 /n+1  + C
• ∫cos x    = sin x  + C
• ∫sin x    = -cos x  + C
• ∫sec 2 x    = tan x  + C
• ∫cosec 2 x    = -cot x  + C
• ∫sec x tan x    = sec x  + C
• ∫cosec  x cot x    = -cosec x  + C
• ∫dx/√ 1- x 2  = sin -1  x  + C
• ∫dx/√ 1- x 2  = -cos -1  x  + C
• ∫dx/√ 1+ x 2  = tan -1  x  + C
• ∫dx/√ 1+ x 2  = -cot -1  x  + C
• ∫e x   = e x  + C
• ∫a x   = a x / log a + C
• ∫dx/x √ x 2   – 1= sec -1  x  + C
• ∫dx/x √ x 2   – 1= cosec -1  x  + C
• ∫1/x    = log |x| + c
• ∫tan x    = log |sec x| + c
• ∫cot x    = log |sin x| + c
• ∫sec x    = log |sec x + tan x| + c
• ∫cosec x    = log |cosec x – cot x| + c

Integrals of some special function s

•  ∫dx/(x 2   – a 2 ) = 1/2a  log⁡ |(x – a) / (x + a)| + c
•  ∫dx/(a 2   – x 2 ) = 1/2a  log⁡ |(a + x) / (a – x)| + c
• ∫dx / (x 2   + a 2 ) = 1/a  tan (-1) ⁡ x / a + c
• ∫dx / √(x 2   – a 2 ) = log |”x” + √(x 2 -a 2 )| + C
• 1.∫dx / √(a 2   – x 2 ) = sin-1 x / a + c
• ∫dx / √(x 2 + a 2 ) = log |”x” + √(x 2 + a 2 )| + C

Integration by parts

∫() ⁡()  = () ∫ () − ∫( ‘ () ∫() )

To decide first function. We use

I → Inverse (Example sin (-1)  ⁡x)

L → Log (Example log ⁡x)

A → Algebra (Example x 2 , x 3 )

T → Trigonometry (Example sin 2 x)

E → Exponential (Example e x )

E → Exponential (Example e x )

∫ex [f (x) + f ′(x)] dx = ∫ex f(x) dx + C

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