We can use the same trick in reverse too. Take a function, differentiate it, expand into a power series, and integrate. When we integrate, the constant of integration will become the constant term of the series. Lets consider an example. We start with a funciton, integrate it, expand it into a power series, then differentiate to get back to the original function.
Every indefinite integral has a constant of integration.
In particular, when we integrate the series, we can't disregard the constant of integration. It turns out to be constant term of the series. Lets look at an example. We start with a function , and compute its series expansion by the method described above. However, as you can see, it doesn't look llike its too good of a representation.