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Sunday, May 7, 2017

Fundamental formulas on integration

  • (log x) = 1/x ⇒ ∫1/x dx = log |x| + C
  • (ex) = ex ⇒ ex dx = ex + C
  • (-cos x) = sin x ⇒ ∫ sin x dx = - cos x + C
  • (sin x) = cos x ⇒ ∫cos x dx = sinx + C
  • (tanx) = sec²x ⇒ ∫sec²x dx = tanx + C
  • (-cotx) = cosec²x ⇒ ∫cosec²x dx = - cot x + C
  • (sec x) = sec x tan x ⇒ ∫sec x tan x dx = sec x + C
  • (- cosec x) = cosec x cot x ⇒ ∫cosec x cot x dx = - cosec x + C
  • (log sin x) = cot x ⇒ cot x dx = log |sinx| + C
  • (-log cos x) = tan x ⇒ tan x dx = - log |cos x| + C
  • (log (sec x + tan x)) = sec x ⇒ ∫sec x dx = log |sec x + tan x| + C
  •  (log (cosec x – cot x)) = cosec x ⇒ ∫cosec x dx = log |cosec x – cot x| + C

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