What you have done so far looks correct.schapman22 said:Homework Statement
We were given a worksheet to integrate some problems using partial fractions. This one however I cannot figure out what to do with it. This is the problem.
∫(x3-4x2+x+6)/(x2-x+2) dx
The Attempt at a Solution
using long division i got ∫(x-3) + (-4(x-3)/(x2-x+2) dx
split it up into ∫xdx - 3∫dx - 4∫(x-3)/(x2-x+2)
now I don't know what to do with the x2-x+2?
any suggestions on how to proceed from here? Thanks in advance!
Partial fractions are a method used in calculus to simplify the integration of a complex rational function into smaller, easier-to-solve fractions.
Partial fractions are typically used when integrating a rational function that cannot be easily integrated using other methods, such as substitution or integration by parts.
To find the partial fraction decomposition, the rational function is first factored into its irreducible factors. Then, the coefficients of each factor are solved for using a system of equations.
The purpose of using partial fractions is to simplify the integration process of a complex rational function. By breaking it down into smaller fractions, it becomes easier to integrate and can lead to a more accurate solution.
Yes, partial fractions can only be used for rational functions, meaning they must have a polynomial in the numerator and denominator. Additionally, the degree of the numerator must be less than the degree of the denominator for the method to work.