If f and g are two integrable functions and C a constant, then we can derive the rules for the integration of the sum, difference of two functions as well as the multiplication of a function by a constant.
Integral of the sum of two functions
∫[f(x)+g(x)]dx = ∫f(x)dx + ∫g(x)dx
The integral of the sum of two functions is equal to the sum of the integrals of these functions. This rule is valid for the integral of the indefinite sum of functions. The integral of the sum of three functions is equal to the sum of the integrals of these three functions. The integral of the sum of four functions is equal to the sum of the integrals of these four functions. The integral of the sum of n functions is equal to the sum of the integrals of these n functions.
Integral of the difference of two functions
∫[f(x) - g(x)]dx = ∫f(x)dx - ∫g(x)dx
Integral of the product of a constant C by a function
∫(Cf(x)dx) = C∫(x)dx.
