How do you integrate #int (x-1)/( x^4 (x-1)^2)# using partial fractions?
2 Answers
Explanation:
1) I used basic fractions method for integration.
I decomposed integrand into basic fractions,
Set
Set
I took differentiaton both sides,
Set
I took differentiaton both sides,
Set
I took differentiaton both sides,
Set
Thus,
=
=
How about NOT using partial fractions and instead using the binomial theorem (or the sum of geometrical series, same thing) after cancelling the
Explanation:
The binomial expansion above works only for
Using the Binomial Theorem, or sum to infinity of GP with first term 1 and common ratio
Using sum to infinity of GP or binomial theorem:
which is the same as the result for