The integral of the rational function (x^3 - 3x^2 + 4x - 9) / (x^2 + 3) can be solved using polynomial long division. The first step involves dividing x^2 + 3 into x^3 - 3x^2 + 4x - 9, yielding a quotient of x and a remainder that includes additional polynomial terms. This process simplifies the integral into a more manageable form, allowing for straightforward integration of the resulting polynomial. The final solution will involve integrating both the quotient and the remainder separately.
PREREQUISITESStudents studying calculus, particularly those focusing on integration techniques, as well as educators looking for examples of polynomial division in the context of integrals.
Please use parentheses around the entire numerator and the entire denominator.fluxions22 said:Homework Statement
how to solve the integral of x^3 - 3x^2 + 4x -9 / x^2 + 3 dx
Homework Equations
using long division
The Attempt at a Solution
x^2 + 3 divided into x^3 - 3x^2 + 4x -9 I am not sure