Question

What I am doing wrong?
integrate dx/(x^3-4x)

Rewrite denominator as x*(x^2-4) and then use integration by partial fractions.

(A/x) + (Bx+C)/(x^2-4)
1=A*(x^2-4)+(Bx+C)*x
A=-1/4 B=1/4 C=0
After that I have to integrate -1/4*integral dx/x
Result is -1/4ln(x)
Second integral is (1/4*x)/(x^2-4)
As result I get 1/8*ln(x^2-4)
My final result is -1/4ln(x)+1/8*ln(x^2-4)+C
Is my result correct?

Answer 1

x^2 - 4 = (x - 2)(x + 2)

Answer 2

So it becomes A/x + B/(x+2) + C/(x-2)

Answer 3

Can I use (Bx+C)/(x^2-4)?

Answer 4

x(x-2)(x+2)

Answer 5

When I take x(x-2)(x+2) then A=-1/4 B=1/8 C=1/8
and result is \[-1/4*\ln(x)+1/8\ln(x-2)+1/8\ln(x+2)\]

Answer 6

correct