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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