## INTEGRATION

Definition of integration :

A function g(x) is called am anti derivative or integral of a function g(x) on an interval I.

If g'(x)  =  g(x)

for every value of x in I.

If the derivative of a function G(x) with respect to x is g(x) then we can say that integral of g(x) with respect to x is g(x). Now we are going to see formulas in this topic.

∫ xⁿ dx  =  x⁽ⁿ ⁺ ¹⁾/(n + 1) + c

∫ (1/xⁿ) dx  =  -1/(n - 1) x⁽ⁿ⁻¹⁾  + c

∫ (1/x) dx  =  log x  + c

∫ e^(x) dx  =  e^x  + c

∫ a^(x) dx  =  a^x/(log a)  + c

∫ sin x dx  =  -cos x + c

∫ cos x dx  =  sin x + c

∫ cosec 2x dx  =  -cot x  + c

∫ sec2 x dx  =  tan x  + c

∫ sec x tan x dx  =  sec x  + c

∫ cosec x cot x dx  =  -cosec x  + c

∫ 1/(1 + x2) dx  =  tan-1x  + c

∫ 1/ √(1 - x2) dx  =  sin -1x   + c

∫  e (ax+b)  =  (1/a) e (ax+b) + C

∫ (ax+b)ⁿ dx  =  (1/a) (ax + b)(n+1)/(n + 1)   + c

1/(ax+b) dx  =  (1/a) log (ax + b) + c

∫ sin (ax + b) dx  =  -(1/a) Cos (ax + b) + c

∫ cos (ax + b) dx  =  (1/a) Sin (ax + b) + c

∫ sec2 (ax + b) dx  =  (1/a) tan (ax + b) + c

∫ cosec2(ax + b) dx  =  -(1/a) cot (ax + b) + c

∫ cosec (ax+b)cot (ax+b)dx  =  -(1/a)cosec (ax+b) + c

∫ sec (ax+b) tan (ax+b) dx  =  sec (ax+b) + c

∫ 1/1+ (ax)2 dx  =  (1/a) tan-1(ax) + c

∫ 1/[1 - (ax2)] dx = (1/a) Sin-1(ax) + c

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