Since integration is the inverse of differentiation, you can think of integration as “dividing” by d.
J. P. Ballantine  shows that you can formally divide by d and get the correct integral. For example, he arrives at
using long division!
 J. P. Ballantine. Integration by Long Division. The American Mathematical Monthly, Vol. 58, No. 2 (Feb., 1951), pp. 104-105