January 21, 2017

Homework Help: Calc easy

Posted by Ang on Friday, February 23, 2007 at 9:05am.

Having trouble getting the correct solution.
The integral of “x squared” in the numerator and “x squared plus x minus 6” in the denominator.

S X2 / (X2 + x – 6) dx


That's a messy one. According to my table of integrals.
The answer is
-x/6 -(1/72)loge(x^2 +x -6)
+ S dx/(x^2 +x -6)

and the last term is another integral that involves an arctangent.

I am not going to attempt to derive it.

Thanks for trying.
I do have the solution, but I'm stuck on part of ariving at the destination.
x - 9/5 ln !x+3! + 4/5 ln !x-2! + C

The trick may require using the method of partial fractions, whereby
x^2/[(x+3)(x-2)] is rewritten as
1 + (6-x)/(x+3)(x-2)]

The "1" term will lead to the "x" term in the integral.

The technique of partial fractions is then applied to the (6-x)/(x+3)(x-2)] term, leaving you with two terms of the form
(ax + b)/(x + 3) + (cx + d)/(x-2)

Do a search online or in your textbook on the method of parital fractions for additional help.

Thank you! Yes it was the algebraic partial fractions. YES!
Thanks again.

Answer This Question

First Name:
School Subject:

Related Questions

More Related Questions