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Integration formulas

Posted By: Courtney Hughes     Category: C Programming     Views: 3339

Article of integration Formulas.

Integration Formula

Working rules of Integration
? [f(x) + g(x)] dx = ?f(x) dx + ?g(x) dx
?k*f(x) dx = k * ?f(x) dx                       ( k = constant)
? u*v dx = u?v dx - ? [(du/dx)?v dx] dx
a?b f(x) dx = [ F(x) ]ab = F(b) - F(a)
Integration formula
 ? xn dx = x n+1 / n + 1
?n dx = n*x + c          
? 1/x dx = log |x| + c
? cos x dx = sin x + c
? sin x dx = - cos x + c
? sec2x dx = tan x + c
? cosec2x dx = - cot x + c
? sec x * tan x dx = sec x + c
? cosec x * cot x dx = - cosec x + c
? dx / (x2 + a2) = (1/a * tan-1 x/a + c) = (- 1/a * cot-1 x/a + c1)
? dx / sqrt(a2 - x2)  = (sin-1 x/a + c) = (-cot-1 x/a + c1)
? dx / (|x| * sqrt(x2 - a2))  = (1/a * sec-1 x/a + c) = (-1/a * cosec-1 x/a + c1)
? ax dx = (ax / logea) + c
? ex dx = ex + c
? dx / sqrt(x2 +/- a2) = log |x + sqrt(x2 +/- a2)| + c
? dx / (x2 - a2)= ((1/(2*a)) * log | (x-a) / (x+a) |  + c
? dx / (a2 - x2)= ((1/(2*a)) * log | (x+a) / (x-a) |  + c
? tan x dx = log |sec x| + c
? cot x dx = log |sin x| + c
? cosec dx = log |tan x/2| + c = log |cosec x - cot x| + c
? sec dx = log |tan (?/4 + x/2)| + c = log |sec x + tan x| + c
?sqrt(x2 + a2) dx = [(x/2) * sqrt(x2 + a2)] + [(a2/2) * log |x + sqrt(x2 + a2)|] + c
?sqrt(x2 - a2) dx = [(x/2) * sqrt(x2 - a2)] - [(a2/2) * log |x + sqrt(x2 - a2)|] + c
?sqrt(a2 -x2) dx = [(x/2) * sqrt(a2-x2)] + [(a2/2) * sin-1 (x/a)] + c
  
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Courtney Hughes
Courtney Hughes author of Integration formulas is from London, United Kingdom.
 
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