The title page of Leonard Euler’s Integral Calculus, vol. 1 (1768). The complete work in three volumes appeared in the interval 1768 – 1770. This was the first complete textbook published on the integral calculus. The entire Integral Calculus is available at the Euler Archive.
Euler’s discussion on page 121 of volume 1 of his Integral Calculus concerning the integration of logarithmic and exponential functions. Note that Euler used lx to represent what we write as ln(x).
An excerpt, pp. 182–183, from volume 2 of Euler’s Integral Calculus, demonstrating a series solution for a differential equation.