What is to integrate a function?
To integrate a function f(x) means to determine the function F(x), which, when is differentiated, gives back the function f(x). We’ll integrate f(x) = y. Int f(x)dx =Int (2x^3+3x+1) dx/x^4 We’ll apply the linear property of integrals and we’ll get: Int (2x^3+3x+1) dx/x^4 = Int 2x^3dx/x^4 + Int 3xdx/x^4 + Int dx/x^4 We’ll calculate each Integral: We’ll start with Int 2x^3dx/x^4 We’ll reduce like terms: Int 2x^3dx/x^4 = Int 2dx/x Int 2dx/x = 2Int dx/x 2Int dx/x = 2ln x + C Now, we’ll calculate Int 3xdx/x^4.
