Integrate the Taylor series for 1/1 - x term by term, and check if the answer matches the Taylor series for - ln(l - x) (use the results of Section 3.7, Exercise 32).
When a function has a well-behaved Taylor series, we can find a Taylor series for some integrals by integrating term by term (proving that these integrals converge to the correct answer requires methods from more advanced courses).