# Thread: Help with Partial Fraction Integration Problem

1. ## Help with Partial Fraction Integration Problem

Sorry, I'm new here and I don't know if there's an easy way to do the math symbols on here or not.

The original problem is to find the integral from 0 to 1 of (2*x^2 - x + 4)/((x^3 - 8)(x^2 - 49)).

I got it worked out to it equaling the integral from 0 to 1 of (-0.04243739*x^2 + 0.01347961*x - 0.0794319)/(x^3 - 8) + (0.02025586)/(x - 7) + (0.02218152)/(x + 7), which matches what is in my workbook, but past that I can't figure out what to do. The book just gives the answer as approx. 0.0111 after this.

To solve the integral from 0 to 1 of (-0.04243739*x^2 + 0.01347961*x - 0.0794319)/(x^3 - 8) would I need to use integration by parts?

And then for the integral from 0 to 1 of (0.02025586)/(x - 7) I am also stuck, since I cannot do 0.02025586*(ln(1-7) - ln(0-7)) because I'd be taking the natural log of a negative number.

If anyone could shed some light on this for me, that would be fantastic. Thank you so much!

2. Originally Posted by Kristen
Sorry, I'm new here and I don't know if there's an easy way to do the math symbols on here or not.

The original problem is to find the integral from 0 to 1 of (2*x^2 - x + 4)/((x^3 - 8)(x^2 - 49)).

I got it worked out to it equaling the integral from 0 to 1 of (-0.04243739*x^2 + 0.01347961*x - 0.0794319)/(x^3 - 8) + (0.02025586)/(x - 7) + (0.02218152)/(x + 7), which matches what is in my workbook, but past that I can't figure out what to do. The book just gives the answer as approx. 0.0111 after this.

To solve the integral from 0 to 1 of (-0.04243739*x^2 + 0.01347961*x - 0.0794319)/(x^3 - 8) would I need to use integration by parts?

And then for the integral from 0 to 1 of (0.02025586)/(x - 7) I am also stuck, since I cannot do 0.02025586*(ln(1-7) - ln(0-7)) because I'd be taking the natural log of a negative number.

If anyone could shed some light on this for me, that would be fantastic. Thank you so much!

Bless your heawrt, this problem is completely insane (unless I missed some trick, which I don't really think so since it is simply rational functions), and the numbers involved in it make it a problem that may take above 40 minutes at least to do if you don't make any mistake in the way and you know perfectly well all your
theory....

Anyway, the denominator is just $\displaystyle (x-2)(x^2+2x+4)(x-7)(x+7)$ , so this already is a mess...good luck!

Tonio

3. Originally Posted by tonio
Bless your heawrt, this problem is completely insane (unless I missed some trick, which I don't really think so since it is simply rational functions), and the numbers involved in it make it a problem that may take above 40 minutes at least to do if you don't make any mistake in the way and you know perfectly well all your
theory....

Anyway, the denominator is just $\displaystyle (x-2)(x^2+2x+4)(x-7)(x+7)$ , so this already is a mess...good luck!

Tonio
I did it with the denominator being $\displaystyle (x^3 - 8)(x-7)(x+7)$, which also works, correct? Would it be easier using the denominator you used?

I am just stuck at the two parts i listed.

The integral from 0 to 1 of $\displaystyle (-0.04243739*x^2 + 0.01347961*x - 0.0794319)/(x^3 - 8)$ and...
the integral from 0 to 1 of $\displaystyle (0.02025586)/(x - 7)$.