Partial fractions integral homework problem: x^5 - 2x^4 + 3x^3 + x - 1 / x^3 - x^2 +

[Matthewabernasty]

Hello this is my first post. I have used the site for knowledge base purposes in the past. My problem is below. I assume to use partial fractions. Find values for A B C and put these values over denominators I find from factoring my original denominator to make use of the partial fractions formula for integration.

Evaluate : Integrand: x^5 - 2x^4 + 3x^3 + x - 1 / x^3 - x^2 + x - 1 (dx)

I tried to solve this my values were A=0 B=0 C=1 I do not believe these are the correct values to use.

Any help is appreciated.

 

[stapel]

Hello this is my first post. I have used the site for knowledge base purposes in the past. My problem is below. I assume to use partial fractions. Find values for A B C and put these values over denominators I find from factoring my original denominator to make use of the partial fractions formula for integration.

The lack of punctuation makes the above difficult to read. I think you're saying that you believe that you're likely expected to break apart the integrand, using the technique of partial-fraction decomposition (wherein "A", "B", and "C" are commonly used as placeholders for constants).

Evaluate : Integrand: x^5 - 2x^4 + 3x^3 + x - 1 / x^3 - x^2 + x - 1 (dx)

I tried to solve this my values were A=0 B=0 C=1 I do not believe these are the correct values to use.

Please reply showing your work (how you got your values) and explaining why you feel that your values are incorrect. When you reply, please include clarification of the integrand. In particular, you have posted this as being the integrand:

. . . . .\(\displaystyle x^5\, -\, 2x^4\, +\, 3x^3\, +\, x\, -\, \dfrac{1}{x^3}\, -\, x^2\, +\, x\, -\, 1\)

Lacking grouping symbols, this is the correct interpretation. However, I strongly suspect that this is incorrect...?

 

[HallsofIvy]

If you mean \(\displaystyle \frac{ x^5 - 2x^4 + 3x^3 + x - 1}{x^3 - x^2 + x - 1}\) (you should have written (x^5 - 2x^4 + 3x^3 + x - 1) / (x^3 - x^2 + x - 1) with the parentheses) then you have an "improper fraction" (the numerator is of higher degree than the denominator) so you need to do the division. You will get a quadratic function plus a quadratic function over \(\displaystyle x^3- x^2+ x- 1\). You can the write the last fraction in terms of partial fractions.

What did you get for the factors of the denominator?