How do you integrate #int (5x - 4 ) / (x^2 -4x) dx# using partial fractions?
Use partial fractions to give the expression in a form that you can integrate, and then integrate it normally.
Initially, ignore the fact that you will be integrating.
Factorise the denominator:
Then multiply by the denominator of
This causes the cancellation of some terms:
For the constant terms:
Now we have everything we need to form our partial fraction:
We are now ready to integrate.
It is easier to see if we separate the two parts of the integration:
These both integrate in the same manner, using the standard antiderivative rule:
So we get the answer: