Finding a certain antiderivative
The problem says:
If find a function g with ..
This problem is stated in the differentiation part of the book, integration comes later.
I tried starting with a simple example and trying to find a pattern from there:
Then we can try:
Then if .
Which is not what I wanted. The denominator in the second summand is ok, but the numerator is not what I need.
But I'm stuck on what I need to look for, any hints for deriving the correct pattern would be appreciated.