# Partial Fractions problem not matching Wolfram Alpha

1. May 19, 2012

### anniecvc

1. The problem statement, all variables and given/known data
∫10x-2x2/((x-1)2(x+3))

Solve by partial fractions.

3. The attempt at a solution

∫A/(x-1) +B/(x-1)2 + C(x+3)

after setting up the partial fractions and multiplying each term by LCD:

10x-2x2= A(x-1)(x+3) + B(x+3) + C(x-1)2

10x-2x2= A(x2+2x-3) +Bx+3B +Cx-C

10x-2x2= Ax2+2Ax-3A+Bx+3B+Cx-C

10x-2x2= x2(A+C) +x(2A+B-2C) + (3B+C-3A)

System of Equations:

A+C = -2
2A+B-2C=10
3B+C-3A =0

Solving these, I get A=23. B=14. C=25.

Putting them back in their partial fractions form and integrating I get:

23*lnlx-1l - 14/(x-1) + 25*lnlx+3l

However Wolfram gives me essentially the same terms but different coefficients: http://www.wolframalpha.com/input/?i=integral+of+%2810x-2x%5E2%29%2F%28%28x-1%29%5E2*%28x%2B3%29%29

What am I doing wrong???

2. May 19, 2012

### vela

Staff Emeritus
You're not solving for A, B, and C correctly. Your equations are fine, but your numerical answers are not. You can easily see this by plugging the results you got for A and C into the first equation.

3. May 19, 2012

### anniecvc

THANK YOU! Got the right answer now. Algebra...a slippery fooler.