Thread: evaluate the integral using partial fractions

1. evaluate the integral using partial fractions

The equation is integral sign ("S") (x^3 -4x^2 + 3x + 7)/(x^2 -3x +2) dx

So first I did the long division and I got

the original equation = S (x - 1 + (9-2x)/(x^2-3x+2)) dx

so 9-2x = A + B
____ __ ___
(x-1)(x-2) (x-1) (x-2)

9-2x = A (x-2) + B(x-1)

so if x = 1 then A = -7 and if x = 2 then B = 5

which gives us

S (x-1- 7/(x-2) + 5/(x-1)) dx = (1/2)x^2 -x -7 ln(x-2) + 5 ln (x-1) +C

Did I do this correctly? I don't like ln but I am assuming I bring the costant infront?

Thanks
Calculus Beginner

2. You are correct all the way until $-7\ln|x-2|+5\ln|x-1|$, which should be $5\ln|x-2|-7\ln|x-1|$.

3. Originally Posted by calcbeg
The equation is integral sign ("S") (x^3 -4x^2 + 3x + 7)/(x^2 -3x +2) dx

So first I did the long division and I got

the original equation = S (x - 1 + (9-2x)/(x^2-3x+2)) dx

so 9-2x = A + B
____ __ ___
(x-1)(x-2) (x-1) (x-2)

9-2x = A (x-2) + B(x-1)

so if x = 1 then A = -7 and if x = 2 then B = 5

which gives us

S (x-1 + 5/(x-2) - 7/(x-1)) dx = (1/2)x^2 -x + 5ln|x-2| - 7ln|x-1| +C
corrections