## Differentiation and Integration Important Formulas (Advance Math)

### Integration Basic Formulas

• ∫cosec 2 x    = -cot x  + C
• ∫sec x tan x    = sec x  + C
• ∫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  x cot x    = -cosec x  + C
• ∫dx/√ 1- x 2  = sin -1  x  + C
• ∫dx/√ 1- x 2  = -cos -1  x  + 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
• ∫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

### Integrals of some special functions (Advance Math)

• ∫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 ) = 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

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