Gottfried Wilhelm Leibniz carried on an active correspondence within the intellectual community of his time. In particular, two of his main correspondents were the brothers Jacob and Johann Bernoulli. Johann began corresponding with Leibniz in 1693. Depicted is the title page of the 1745 edition of the Leibniz Bernoulli Correspondence, vol.1. This book contains their correspondence for the years 1694 - 1699.
This is from a letter of June, 1695 in which Leibniz is discussing differentiation with Johann Bernoulli. Notice that Leibniz sometimes uses negative powers on the "d" to represent anti-differentiation.
In this letter from December, 1696 from Leibniz to Bernoulli there is a discussion of integration by parts applied to functions having powers of x and powers of the logarithm.