beaf123 said:Homework Statement
∫ (x^3)/(x^2+2x+1) dx
I think I could solve it if I knew how they did this operation:
From the solution:
'
(x^3)/(x^2+2x+1) = (x-2) + (3x+2)/(x+1)^2 ( After long division)
Did they use polynomial division?
x^3: x^2-2X+1=
If so, how?
Polynomial division is a method used to divide polynomials, which are algebraic expressions with one or more terms that can include variables, constants, and exponents. It involves breaking down a polynomial into simpler, smaller parts.
To solve partial fractions with polynomial division, you first need to factor the denominator of the fraction into its irreducible factors. Then, you set up a system of equations with the partial fractions on one side and the original fraction on the other side. Finally, you solve for the unknown coefficients by equating the corresponding terms on both sides of the equation.
Polynomial division is used in partial fractions because it allows us to break down a complex fraction into smaller, simpler fractions. This makes it easier to integrate or manipulate the original fraction in algebraic equations.
The steps involved in solving partial fractions with polynomial division are: 1) Factor the denominator of the fraction into its irreducible factors. 2) Set up a system of equations with the partial fractions on one side and the original fraction on the other side. 3) Solve for the unknown coefficients by equating the corresponding terms on both sides of the equation.
No, polynomial division can only be used to solve fractions where the denominator is a polynomial. It is not applicable to fractions with other types of expressions, such as radicals or trigonometric functions.