Problem

$\displaystyle \int\frac{10x-2x^2}{(x-1)^2(x+3)}$

I did all the steps correctly until this part

A+C = -2

2A+ B -2C = 10

-3A +3B + C = 0

Attempt:

I said C = -A-2

B = -2A +2C + 10

So

-3A + 3(2A + 2(-A-2) + 10) + (-A-2) = 0

-3A + 3(2A -2A -4 + 10) -A-2 = 0

-3A + -12 +30 -A - 2 = 0

-4A +16 = 0

-4A = -16

Answer:

A = 4

Correct Answer

A= 1, B= 2, C= -3

*This is related to partial fractions in Calculus.