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.

Formulas:

∫ 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 ² x dx = - Cot x + c

∫ Sec ² x dx = tan x + c

∫ sec x tan x dx = sec x + c

∫ Cosec x cot x dx = - Cosec x + c

∫ 1/(1 + x ²) dx = tan ⁻ ¹x + c

∫ 1/ √(1 - x ²) dx = Sin ⁻ ¹x + c

∫ e^(a x + b) = (1/a) e^ (a x + 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

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

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

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

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

∫ Cosec ² (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 - (ax ²)] dx = (1/a) Sin ⁻ ¹(ax) + c

Related pages

SBI!