How do you use partial fraction decomposition to decompose the fraction to integrate #(16x^4)/(2x-1)^3#?
First do the division, then decompose the remainder term.
We can do a partial fraction decomposition only if the degree of the numerator is less than that of the denominator.
So for this question, we start by dividing
# = 2x+3+(24x^2-16x+3)/(2x-1)^3#
We can easily integrate
Leads (after some algebra) to:
So we get: