(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

∫10x-2x^{2}/((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-2x^{2}= A(x-1)(x+3) + B(x+3) + C(x-1)^{2}

10x-2x^{2}= A(x^{2}+2x-3) +Bx+3B +Cx-C

10x-2x^{2}= Ax^{2}+2Ax-3A+Bx+3B+Cx-C

10x-2x^{2}= x^{2}(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???

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Partial Fractions problem not matching Wolfram Alpha

**Physics Forums | Science Articles, Homework Help, Discussion**