How do you find int (x - 4 ) / (x^2 -4x) dx using partial fractions?

2 Answers
Nov 4, 2015

int (x-4)/(x^2-4x)dx = ln |x|

Explanation:

int (x-4)/(x^2-4x)dx = int (x-4)/(x(x-4))dx = int 1/x dx = ln |x|

Nov 4, 2015

Reduce the fraction.

Explanation:

When you factor the denominator to start the partial fraction decomposition, note that the ratio can be reduced.

int (x-4)/(x^2-4x) dx = int (x-4)/(x(x-4)) dx

= int 1/x dx = lnabsx +C

If you didn't notice it could be reduced, find A, "and " B so that:

A/x + B/(x-4) = (x-4)/(x(x-4))

So Ax-4A+Bx = x-4

And A+B=1

and -4A=-4, " " so A=1 and B=0