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Math Shortcut Tricks- Differentiation Integration in Calculus Formulas

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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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